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Right Triangle Trigonometry (Section 4-3). Find the exact values of the six trigonometric functions of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.). Example 1:. sin θ = csc θ = cos θ = sec θ = tan θ = cot θ =. 4. θ.

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## Right Triangle Trigonometry (Section 4-3)

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**Find the exact values of the six trigonometric functions of**the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Example 1: sin θ = cscθ = cosθ = sec θ = tan θ = cot θ = 4 θ 3**Sketch a right triangle corresponding to the trigonometric**function of the acute angle θ. Use the Pythagorean Theorem to determine the third side of the triangle and then find the other five trigonometric functions of θ. Example 2**Sketch a right triangle corresponding to the trigonometric**function of the acute angle θ. Use the Pythagorean Theorem to determine the third side of the triangle and then find the other five trigonometric functions of θ. Example 3**30-60-90**45-45-90 60° 2 45° 1 1 30° 45° 1**Construct an appropriate triangle to complete the table. (0**<θ< 90°, ) Example 4 Function θ(deg) θ (rad) Function Value cos 60° 60° 2 1 30°**Construct an appropriate triangle to complete the table. (0**<θ< 90°, ) Example 5 Function θ(deg) θ (rad) Function Value csc 45° 1 45° 1**Construct an appropriate triangle to complete the table. (0**<θ< 90°, ) Example 6 Function θ(deg) θ (rad) Function Value tan 60° 2 1 30°**Complete the identity.**Example 7**Use the given function value(s) and the trigonometric**identities to find the indicated trigonometric functions. Example 8 tan 60° b) sin 30 ° c) cos 30 ° d) sec 60 °**Use the given function value(s) and the trigonometric**identities to find the indicated trigonometric functions. Example 9 sec α b) sin α c) cot α d) sin (90 ° - α)**Use trigonometric identities to transform one side of the**equation into the other (0<θ<π/2). Example 10 cosθ sec θ = 1**Use trigonometric identities to transform one side of the**equation into the other (0<θ<π/2). Example 11 (sec θ + tan θ)(sec θ – tan θ) = 1**Use trigonometric identities to transform one side of the**equation into the other (0<θ<π/2). Example 12**Use a calculator to evaluate each function. (Be sure your**calculator is in the correct angle mode) Example 13 cos 14°**Use a calculator to evaluate each function. (Be sure your**calculator is in the correct angle mode) Example 14 csc 18°51’**Use a calculator to evaluate each function. (Be sure your**calculator is in the correct angle mode) Example 15**Find each value of θ in degrees (0°< θ < 90°) and**radians (0 < θ < π/2) without using a calculator. Example 16**Find each value of θ in degrees (0°< θ < 90°) and**radians (0 < θ < π/2) without using a calculator. Example 17**30-60-90**45-45-90 60° 2 45° 1 1 30° 45° 1**Find the exact values of the indicated variables (selected**from x, y, and r) Example 18 Find y and r. r y 30° 100**Find the exact values of the indicated variables (selected**from x, y, and r) Example 19 Find x and r. r 45° x**Example 20 A surveyor is standing 50 feet from the base of**a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree?**Example 21 You are 200 yards from a river. Rather than**walking directly to the river, you walk 400 yards along a straight path to the river’s edge. Find the acute angle θ between this path and the river’s edge.**Example 22 Find the length of c of the skateboard ramp with**a height of 4 ft and an angle of elevation of 18.4°.**HW #14 pg 284 – 285 (1- 41 odd)**HW #15 pg 285 (43 – 47 odd, 49 – 56 all, 57 – 61 odd) HW #16 pg 285 – 286 (63 – 81 odd)

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