AP EAMCET · Maths · Trigonometric Ratios & Identities

Let $θ$ be an angle in the standard position such that the point $(- 5, 12)$ lies on its terminal side, then

A $| \sin θ | = - \sin θ$
B $| \cos θ | = \cos θ$
C $| \tan θ | = - \tan θ$
D $| cosec θ | = - cosec θ$

Verified Solution

Answer & Solution

Correct Answer

(C) $| \tan θ | = - \tan θ$

Step-by-step Solution

Detailed explanation

Clearly, the point -5,12 lies in second quadrant. Since, it's x-coordinate is negative and y-coordinate is positive. We know that, in second quadrant sinθ & cosecθ are positive and cosθ, secθ, tanθ & cotθ are…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Let θ be an angle in the standard position such that the point (-5,12) lies on its terminal side, then

Step-by-step Solution

Let $θ$ be an angle in the standard position such that the point $(- 5, 12)$ lies on its terminal side, then