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1212If \u03B8 is an obtuse angle and in Quadrant III, what is ?

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Question:

A
1212

explanation

1212Use the trigonometric identity to solve for , then use the Quadrant information to solve for , which can then be used to find and .

Substitute the into the trigonometric identity:

, which becomes

, so .

Evaluate the square root to find sin\u03B8:

. It is given that the cosine value is in Quadrant III, so the sine value is negative and equals .

Recall that and . Substitute the appropriate values to find tangent and secant:

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