3. Unit Circle
Trigonometric Functions on the Unit Circle
3. Unit Circle
Trigonometric Functions on the Unit Circle - Video Tutorials & Practice Problems
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Sine, Cosine, & Tangent on the Unit Circle
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Problem
ProblemFind the sine, cosine, and tangent of each angle using the unit circle.
θ=−1.18 rad, (135,−1312)
A
B
sinθ=−1312,cosθ=135,tanθ=−512
C
sinθ=1312,cosθ=135,tanθ=125
D
sinθ=135,cosθ=13−12,tanθ=125
3
Problem
ProblemFind the sine, cosine, and tangent of each angle using the unit circle.
θ=225°,(−22,−22)
A
sinθ=−22,cosθ=−22,tanθ=2
B
sinθ=22,cosθ=−22,tanθ=−1
C
sinθ=−22,cosθ=−22,tanθ=1
D
sinθ=22,cosθ=22,tanθ=12
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PRACTICE PROBLEMS AND ACTIVITIES (52)
- Find exact values of the six trigonometric functions for each angle A.
- CONCEPT PREVIEW Match each trigonometric function in Column I with its value in Column II. Choices may be used...
- Find each exact function value. See Example 2. ...
- Graph each function over a one-period interval.y = - (1/2) csc (x + π/2)
- CONCEPT PREVIEW Match each trigonometric function in Column I with its value in Column II. Choices may be used...
- Find one solution for each equation. Assume all angles involved are acute angles. cos(3θ + 11°) = sin( 7θ + ...
- Find exact values or expressions for sin A, cos A, and tan A. See Example 1.
- Find exact values or expressions for sin A, cos A, and tan A. See Example 1.
- Determine whether each statement is true or false. If false, tell why. tan 60° ≥ cot 40°
- Determine whether each statement is true or false. If false, tell why. csc 22° ≤ csc 68°
- Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Use the Pythagorean...
- Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Use the Pythagorean...
- Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Use the Pythagorean...
- In Exercises 17–20, θ is an acute angle and sin θ and cos θ are given. Use identities to find tan θ, csc θ, se...
- Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Use the Pythagorean...
- In Exercises 17–20, θ is an acute angle and sin θ and cos θ are given. Use identities to find tan θ, csc θ, se...
- In Exercises 21–24, θ is an acute angle and sin θ is given. Use the Pythagorean identity sin²θ + cos²θ = 1 to ...
- Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. s...
- In Exercises 21–24, θ is an acute angle and sin θ is given. Use the Pythagorean identity sin²θ + cos²θ = 1 to ...
- In Exercises 25–30, use an identity to find the value of each expression. Do not use a calculator. sin 37° cs...
- Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. t...
- In Exercises 28–29, find a cofunction with the same value as the given expression. sin 70°
- In Exercises 25–30, use an identity to find the value of each expression. Do not use a calculator. sin² 𝜋 + ...
- Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. c...
- In Exercises 25–30, use an identity to find the value of each expression. Do not use a calculator. sec² 23° -...
- In Exercises 31–38, find a cofunction with the same value as the given expression. sin 7°
- Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. tan α = cot(...
- In Exercises 31–38, find a cofunction with the same value as the given expression. csc 25°
- Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. sin(2θ + 10°...
- In Exercises 31–38, find a cofunction with the same value as the given expression. tan 𝜋 9
- Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. cot(5θ + 2°)...
- In Exercises 31–38, find a cofunction with the same value as the given expression. cos 2𝜋 5
- Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. cos(2θ + 50°...
- Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. sec(3β + 10°...
- Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. csc(β + 40°)...
- In Exercises 41–43, find the exact value of each of the remaining trigonometric functions of θ. cos θ = 2/5, ...
- Determine whether each statement is true or false. See Example 4. tan 28° ≤ tan 40°
- Determine whether each statement is true or false. See Example 4. cos 28° < sin 28° (Hint: sin 28° = cos ...
- Determine whether each statement is true or false. See Example 4. cot 30° < tan 40°
- Determine whether each statement is true or false. See Example 4. csc 20° < csc 30°
- Give the exact value of each expression. See Example 5. tan 30°
- Give the exact value of each expression. See Example 5. sin 30°
- Give the exact value of each expression. See Example 5. cos 30°
- Give the exact value of each expression. See Example 5. sec 45°
- Give the exact value of each expression. See Example 5. cot 45°
- Give the exact value of each expression. See Example 5. csc 60°
- Concept Check Work each problem. Find the equation of the line that passes through the origin and makes a 30°...
- Concept Check Work each problem. What angle does the line y = √3x make with the positive x-axis?
- Find the exact value of the variables in each figure.
- Find the exact value of the variables in each figure.
- Find a formula for the area of each figure in terms of s.
- Find a formula for the area of each figure in terms of s.