Question

If tan theta = 12/5 and cos theta= -5/13 then what is sin theta?

Answer 1

• - 12/13

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To find sin theta, we can use the identity:

• sin² θ + cos² θ = 1

We know cos θ, so we can solve for sin θ:

• sin² θ + (-5/13)² = 1
• sin² θ + 25/169 = 1
• sin² θ = 144/169
• sin θ = ± 12/13

Since tan θ is positive and cos θ is negative, sin θ must be negative as:

• tan θ = sin θ / cos θ

Therefore, the answer is:

• sin θ = - 12/13