Question

1. Trig Function

Answer 1

The values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trigonometric functions

From the question, we are to determine the values of the given trig functions in terms of sinθ and/or cosθ

• sinθ

NOTE: tanθ = sinθ / cosθ

∴ sinθ = tanθ.cosθ

• cosθ

From above, we can write that

cosθ = sinθ/tanθ

• secθ

Secant is the inverse of cosine

∴ secθ = 1/cosθ

• cscθ (cosecθ)

Cosecant is the inverse of sine

∴ cscθ = 1/sinθ

• tanθ

tanθ = sinθ/cosθ

• cotθ

Cotangent is the inverse of tangent
∴ cotθ = 1/tanθ

But, tanθ = sinθ/cosθ

∴ cotθ = cosθ/sinθ

Hence, the values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Learn more on Trigonometric functions here: brainly.com/question/10316891

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