Assume that theta is a positive acute angle. Given: sin theta=40/41
Find: cos2theta

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Step-by-step explanation:sin

(

θ

)

=

40

41

Use the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

sin

(

θ

)

=

opposite

hypotenuse

Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.

Adjacent

=

√

hypotenuse

2

−

opposite

2

Replace the known values in the equation.

Adjacent

=

√

(

41

)

2

−

(

40

)

2

Simplify

√

(

41

)

2

−

(

40

)

2

.

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Adjacent

=

9

Find the value of cosine.

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cos

(

θ

)

=

9

41

Find the value of tangent.

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tan

(

θ

)

=

40

9

Find the value of cotangent.

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cot

(

θ

)

=

9

40

Find the value of secant.

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sec

(

θ

)

=

41

9

Find the value of cosecant.

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csc

(

θ

)

=

41

40

This is the solution to each trig value.

sin

(

θ

)

=

40

41

cos

(

θ

)

=

9

41

tan

(

θ

)

=

40

9

cot

(

θ

)

=

9

40

sec

(

θ

)

=

41

9

csc

(

θ

)

=

41

40

d

step-by-step explanation: