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 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 30° 60° 1 2 45° 1

Construct an appropriate triangle to complete the table Example 4 Function θ(deg) θ (rad) Function Value cos 60° 30° 60° 1 2

Construct an appropriate triangle to complete the table Example 5 Function θ(deg) θ (rad) Function Value csc 45° 1

Construct an appropriate triangle to complete the table Example 6 Function θ(deg) θ (rad) Function Value tan 30° 60° 1 2

Complete the identity. Example 7

Cofunctions of complementary Angles are Equal

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 cos θ 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 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 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 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 30° 60° 1 2 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 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)