Sketch a right triangle corresponding to the trigonometric function of the acute

Question

Sketch a right triangle corresponding to the trigonometric function of the acute angle ?. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of ?.

sin(?) = 20/29

Part 1 of 4

First construct a right triangle having ? as one of the acute angles.

Consider the trigonometric functionsin(?) =

.

Recall that sin(?) =

.

Find the value of x, y and z in the right triangle that corresponds to the given trigonometric function.

20

29

unknown

Part 2 of 4

By the Pythagorean Theorem,

(hyp)2 = (opp)2 + (adj)2

y

x

)2 + (z)2

Part 3 of 4

29

20

400

)Simplify and find the value of z.z =

400

=

441

21

.

Part 4 of 4

Therefore, the other trigonometric functions of ? are as follows.

Explanation / Answer

z=21

cos?=20/29=0.6896

tan?=21/20=1.05

sec?= 29/20=1.45

cosec?= 29/21=1.38

cot?= 20/21=0.952

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