Find the exact values of a) sec of theta b)tan of theta if cos of theta= -4/5 and sin< 0

Using trigonometric ratio:

From the given statement:

and sin < 0

⇒ lies in the 3rd quadrant.

then;

Using trigonometry identities:

Substitute the given values we have;

Since, sin < 0

⇒

now, find :

Substitute the given values we have;

Therefore, the exact value of:

(a)

(b)

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2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.