Right Triangle Trigonometry (Section 4-3)

Transcription

1 Right Triangle Trigonometry (Section 4-3) Essential Question: How does the Pythagorean Theorem apply to right triangle trigonometry? Students will write a summary describing the relationship between the Pythagorean Theorem and right triangle trigonometry.

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4 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: 4 sin θ = csc θ = cos θ = sec θ = 3 θ tan θ = cot θ =

5 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 sin 3

6 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 sec 10 9

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8 Construct an appropriate triangle to complete the table. (0 < θ < 90, 0 ) Example 4 Function θ(deg) θ (rad) Function Value cos

9 Construct an appropriate triangle to complete the table. (0 < θ < 90, 0 ) Example 5 Function θ(deg) θ (rad) Function Value csc

10 Construct an appropriate triangle to complete the table. (0 < θ < 90, 0 ) Example 6 Function θ(deg) θ (rad) Function Value tan

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12 Complete the identity. Example 7 1 cos sin cos 1 cot

13 sin 30 1, cos 60 1 sin 60 3, cos30 3 Cofunctions of complementary Angles are Equal sin tan sec 90 cos cos 90 sin 90 cot cot 90 tan 90 csc csc 90 sec

14 Use the given function value(s) and the trigonometric identities to find the indicated trigonometric functions. Example 8 sin 60 3, cos 60 1 a) tan 60 b) sin 30 c) cos 30 d) sec 60

15 Use the given function value(s) and the trigonometric identities to find the indicated trigonometric functions. Example 9 tan 3 a) sec α b) sin α c) cot α d) sin (90 - α)

16 Homework: Page #1-47 odd

17 Use trigonometric identities to transform one side of the equation into the other (0<θ<π/). Example 10 cos θ sec θ = 1

18 Use trigonometric identities to transform one side of the equation into the other (0<θ<π/). Example 11 (sec θ + tan θ)(sec θ tan θ) = 1

19 Use trigonometric identities to transform one side of the equation into the other (0<θ<π/). Example 1 1 cot 1 sin

20 Use a calculator to evaluate each function. (Be sure your calculator is in the correct angle mode) Example 13 cos 14

21 Use a calculator to evaluate each function. (Be sure your calculator is in the correct angle mode) Example 14 csc 18 51

22 Use a calculator to evaluate each function. (Be sure your calculator is in the correct angle mode) Example 15 cot 1

23 Find each value of θ in degrees (0 < θ < 90 ) and radians (0 < θ < π/) without using a calculator. Example 16 cos 1

24 Find each value of θ in degrees (0 < θ < 90 ) and radians (0 < θ < π/) without using a calculator. Example 17 sin

25 hyp short long short 3 hyp leg

26 Find the exact values of the indicated variables (selected from x, y, and r) Example 18 Find y and r. r y

27 Find the exact values of the indicated variables (selected from x, y, and r) Example 19 Find x and r. r 3 45 x

28 Example 0 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 How tall is the tree?

29 Example 1 You are 00 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.

30 Example Find the length of c of the skateboard ramp with a height of 4 ft and an angle of elevation of 18.4.

31 HW #9 pg 85, all, odd) HW #10 pg (63 81 odd)