Question

If cos(θ) = 6/8 and θ is in the IV quadrant, then fine:

(a) tan(θ)cot(θ)

(b) csc(θ)tan(θ)

(c) sin^2(θ) + cos^2(θ)

Answer 1

a) 1

b)
`(4)/(3)`

c) = 1

Explanation:

We are given the following in the question:

`\cos \theta = (6)/(8)`

θ is in the IV quadrant.

`\sin^2 \theta + \cos^2 \theta = 1\\\\\sin \theta = \sqrt{1-(36)/(64)} = -(2\sqrt7)/(8)\\\\\tan \theta = (\sin \theta)/(\cos \theta) = -(2\sqrt7)/(6)\\\\\csc \theta = (1)/(\sin \theta) = -(8)/(2\sqrt7)`

Evaluate the following:

a)

`\tan \theta* \cot \theta =\tan \theta*(1)/(\tan \theta) = 1`

b)

`\csc \theta* \tan \theta\\\\= -(8)/(2\sqrt7)* -(2\sqrt7)/(6) = (4)/(3)`

c)

`\sin^2 \theta + \cos^2 \theta = 1\\\text{using the trignometric identity}`