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Precalculus: Trigonometric Functions and Laws

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Terms in this set (20)

  • What is the sine function in trigonometry?

    The sine function relates an angle of a right triangle to the ratio of the length of the opposite side over the hypotenuse.

  • Define the cosine function.

    The cosine function relates an angle of a right triangle to the ratio of the adjacent side length over the hypotenuse.

  • What does the tangent function represent?

    The tangent function is the ratio of the opposite side to the adjacent side in a right triangle.

  • State the Law of Sines formula.

    The Law of Sines states: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\), relating sides and opposite angles in any triangle.

  • When is the Law of Sines used?

    Use the Law of Sines to find unknown sides or angles in any triangle when you know either two angles and one side or two sides and a non-included angle.

  • State the Law of Cosines formula.

    The Law of Cosines is: \(c^2 = a^2 + b^2 - 2ab \cos C\), relating sides and the included angle in any triangle.

  • When is the Law of Cosines applied?

    Use the Law of Cosines to find a side when two sides and the included angle are known, or to find an angle when all three sides are known.

  • What is the period of the sine and cosine functions?

    The period of sine and cosine functions is \(2\pi\), meaning the functions repeat every \(2\pi\) radians.

  • How do you find the amplitude of a trigonometric function?

    The amplitude is the absolute value of the coefficient before sine or cosine, representing the maximum value of the function.

  • What is the general form of a sine function?

    The general form is \(y = A \sin(Bx + C) + D\), where A is amplitude, B affects period, C is phase shift, and D is vertical shift.

  • How do you calculate the period of \(y = \sin(Bx)\)?

    The period is \(\frac{2\pi}{|B|}\), where B is the coefficient of x inside the sine function.

  • What is the phase shift in a trigonometric function?

    The phase shift is the horizontal shift of the graph, calculated by \(-\frac{C}{B}\) in \(y = A \sin(Bx + C) + D\).

  • Explain the vertical shift in trigonometric functions.

    The vertical shift moves the graph up or down by D units in \(y = A \sin(Bx + C) + D\).

  • What is the Pythagorean identity involving sine and cosine?

    The identity is \(\sin^2 \theta + \cos^2 \theta = 1\), true for all angles \(\theta\).

  • How do you convert degrees to radians?

    Multiply degrees by \(\frac{\pi}{180}\\) to convert to radians.

  • How do you convert radians to degrees?

    Multiply radians by \(\frac{180}{\pi}\\) to convert to degrees.

  • What is the sine of 90 degrees or \(\frac{\pi}{2}\) radians?

    Sine 90° or \(\sin \frac{\pi}{2}\) equals 1.

  • What is the cosine of 0 degrees or 0 radians?

    Cosine 0° or \(\cos 0\) equals 1.

  • What is the tangent of 45 degrees or \(\frac{\pi}{4}\) radians?

    Tangent 45° or \(\tan \frac{\pi}{4}\) equals 1.

  • What is the relationship between sine and cosine for complementary angles?

    Sine of an angle equals the cosine of its complement: \(\sin \theta = \cos(90^\circ - \theta)\).