Let Theta be an angle such that secTheta =(5)/(4) and tanTheta lt 0 Find the exact values of cotTheta and cscTheta cotTheta =square cscTheta =square

Question

Let Theta be an angle such that secTheta =(5)/(4) and tanTheta lt 0 Find the exact values of cotTheta and cscTheta cotTheta =square cscTheta =square

Answer 1

To find the exact values of

and

, we can use the given information that

and

.First, let's find

using the reciprocal identity of secant:

Since

, we know that

is in the second or fourth quadrant. In the second quadrant, cosine is positive and sine is positive, while in the fourth quadrant, cosine is positive and sine is negative.Now, let's find

using the Pythagorean identity:

Since

is in the second or fourth quadrant, we need to determine the sign of

. In the second quadrant, sine is positive, so

. In the fourth quadrant, sine is negative, so

.Now, let's find

using the reciprocal identity of tangent:

Since

, we have:

Since

is in the second or fourth quadrant, we need to determine the sign of

. In the second quadrant, cotangent is negative, so

. In the fourth quadrant, cotangent is positive, so

.Finally, let's find

using the reciprocal identity of sine:

Since

is in the second or fourth quadrant, we need to determine the sign of

. In the second quadrant, cosecant is positive, so

. In the fourth quadrant, cosecant is negative, so

.Therefore, the exact values of

and

are:

Problemas

Let Theta be an angle such that secTheta =(5)/(4) and tanTheta lt 0 Find the exact values of cotTheta and cscTheta cotTheta =square cscTheta =square

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