Final answer:
The student asked about finding the other side of a right triangle using sec θ. The correct definition is sec θ = 1/cos θ where secant is reciprocal to cosine. Knowing this enables the calculation of the adjacent side when the hypotenuse is known.
Step-by-step explanation:
The question deals with finding the second side of a right triangle when given sec θ, which is one of the trigonometric functions. To clarify, the correct mathematical identity for secant is sec θ = 1/cos θ. Therefore, the other options provided are incorrect with respect to the definition of secant, as they relate to sine and tangent, which are separate trigonometric functions.
Secant is the reciprocal of cosine, so if one knows the value of secant, they can find the value of cosine by taking its reciprocal. Once cosine is known, the adjacent side of the triangle can be found by multiplying the hypotenuse by the cosine of the angle (adjacent = hypotenuse * cos θ).
The identities given such as sin 2θ, cos 2θ, the law of sines, and law of cosines offer different ways to solve various triangle problems.