Trigonometric Functions on Right Triangles quiz #1 Flashcards
Trigonometric Functions on Right Triangles quiz #1
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What is the tangent (tan) function in trigonometry? The tangent (tan) of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle (tan θ = opposite/adjacent). If you know the radius of a circle, how can you find the length of an arc with a given central angle in degrees? The length of an arc is given by (θ/360) × 2πr, where θ is the central angle in degrees and r is the radius. Given a right triangle DEF, how do you find the sine, cosine, and tangent of an angle? For an angle in triangle DEF, sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, and tangent is opposite/adjacent. What is the general method to find the measure of an angle in a triangle if you know the trigonometric ratio? Use the inverse trigonometric function (arcsin, arccos, or arctan) on the known ratio to find the angle's measure. Which equation can be used to find the length of a side in a right triangle given an angle and the hypotenuse? Use the equation: side = hypotenuse × sin(angle) or side = hypotenuse × cos(angle), depending on whether the side is opposite or adjacent to the angle. How do you find the measure of an angle in a right triangle using the sides? Use the inverse trigonometric function: for example, θ = arcsin(opposite/hypotenuse), θ = arccos(adjacent/hypotenuse), or θ = arctan(opposite/adjacent). Which equation can be used to find the measure of an angle in a right triangle given two sides? Use the inverse trigonometric function: θ = arcsin(opposite/hypotenuse), θ = arccos(adjacent/hypotenuse), or θ = arctan(opposite/adjacent). Given a right triangle JKL, how do you write the trigonometric ratios for angle J? For angle J, sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, and tangent is opposite/adjacent. What is the measure of each angle in a square? Each angle in a square measures 90 degrees. Which equation can be used to find the measure of an angle in a right triangle given the lengths of two sides? Use the inverse trigonometric function: θ = arcsin(opposite/hypotenuse), θ = arccos(adjacent/hypotenuse), or θ = arctan(opposite/adjacent). How do you find the measure of an angle in a triangle if you know the side lengths? Round to the nearest whole degree. Use the appropriate inverse trigonometric function (arcsin, arccos, or arctan) with the given side lengths and round the result to the nearest whole degree. How do you find the measure of an arc in a circle given the central angle in degrees? The measure of the arc in degrees is equal to the measure of the central angle. If angle BAC measures 56 degrees, what is the measure of its supplement? The supplement of angle BAC is 180 - 56 = 124 degrees. How do you determine if two lines are perpendicular based on their slopes? Two lines are perpendicular if the product of their slopes is -1. Given two angles in a triangle, how do you find the third angle? Subtract the sum of the two known angles from 180 degrees to find the third angle. What is the measure of each interior angle in a regular polygon with 8 sides? Each interior angle is [(8-2) × 180] ÷ 8 = 135 degrees. How do you find the vertical change between two points on a coordinate plane? Subtract the y-coordinate of the first point from the y-coordinate of the second point. How do you find the value of an unknown angle in a triangle if the sum of the angles is 180 degrees? Subtract the sum of the known angles from 180 degrees to find the unknown angle. Which trigonometric ratios are correct for a right triangle with sides a, b, and c (c is hypotenuse)? sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent. If two angles in a triangle are equal and the sum of three angles is equal to a fourth angle, what can you conclude? If two angles are equal and the sum of three angles equals a fourth, the triangle is not possible since the sum of angles in a triangle is always 180 degrees. Given two sides of a right triangle, how do you find the trigonometric ratios? Use the definitions: sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent. In which triangle is the value of x equal to arctan(3.1/5.2)? In a right triangle where the side opposite angle x is 3.1 units and the side adjacent to x is 5.2 units, x = arctan(3.1/5.2). How do you find the measure of an angle in a triangle if you know the trigonometric ratio? Use the inverse trigonometric function (arcsin, arccos, or arctan) with the given ratio. What is the measure of each angle in a regular polygon with 4 sides? Each angle in a regular quadrilateral (square) is 90 degrees. If tangent θ = -3/8, what is the value of θ? θ = arctan(-3/8). How do you find the length of an arc in a circle given the circumference and the central angle in degrees? Arc length = (central angle/360) × circumference. Which equation can be used to solve for a side c in a right triangle given an angle and another side? Use c = known side / trigonometric ratio, depending on which sides and angle are given. How do you find the measure of an angle in a triangle using trigonometric ratios? Use the inverse trigonometric function (arcsin, arccos, or arctan) with the appropriate side lengths. If one angle in a triangle is 130 degrees, what can you say about the other angles? The other two angles must sum to 50 degrees, and both must be less than 90 degrees. Which angles in a triangle are congruent to each other? Angles are congruent if they have the same measure. What is the supplement of an angle that measures x degrees? The supplement is 180 - x degrees. Which equation is correct regarding the measure of an angle in a right triangle using trigonometric ratios? The measure of the angle equals the inverse trigonometric function of the appropriate ratio, such as θ = arcsin(opposite/hypotenuse). How do you determine if two lines are perpendicular using their slopes? Two lines are perpendicular if the product of their slopes is -1. Which measurements could represent the side lengths of a right triangle? Any set of three positive numbers that satisfy the Pythagorean theorem: a^2 + b^2 = c^2, where c is the hypotenuse. If a is perpendicular to c, what is the relationship between their slopes? Their slopes are negative reciprocals of each other. Given that cos(θ) = 310/√10, what is the value of θ? θ = arccos(310/√10). What is the general form of a trigonometric function f(x)? A general trigonometric function can be written as f(x) = A sin(Bx + C) + D or f(x) = A cos(Bx + C) + D. Given that sin(θ) = -12/13, what is the value of θ? θ = arcsin(-12/13). In the equation x = a sin(ωt), what do the variables represent? x is the value of the function, a is the amplitude, ω is the angular frequency, and t is the variable (often time). How do you approximate the measure of an angle in a right triangle using trigonometric ratios? Use the inverse trigonometric function on the ratio and round to the nearest degree.
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