The trigonometric function is and  .

Reciprocal identity: .

If , then .

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From Pythagorean theorem,

Since and .

Therefore, lies in second quadrant.

lies in second quadrant, is positive and is negative.

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(a)

Find .

Use Double-angle formula : .

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Substitute and .

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(b) Find .

Use Double-angle formula : .

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Substitute and .

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(c) Find .

Use Half-angle formula: .

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Substitute in above expression.

since lies in  second quadrant,  .

Therefore, is positive.

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(d) Find .

Use Half-angle formula: .

Substitute .

Here , therefore is positive.

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(a) .

(b) .

(c) .

(d) .