55.4k views
2 votes
Let 0 be an angle such that sec0= -13/12 and cot0<0. Find the exact values of tan0 and sin0.

User Adjanaye
by
8.3k points

2 Answers

0 votes

Answer:

tan 0 = -2.4

sin 0 = 0.42

Explanation:

sec 0 = -13/12 => cos 0 = -12/13

cot 0 < 0 => tan 0 < 0

so, the angle is on second quadrant

=> tan 0 = -12/5 = -2.4

=> sin 0 = 5/12 = 0.42

User Fivebob
by
7.9k points
6 votes

Answer:

Solution given;

Sec θ=-
(13)/(12)

cotθ< 0,

It lies in second quadrant.

where sin and cosec is positive.

Now


(1)/(cosθ)=-(13)/(12)

cosθ=
(12)/(13)


(b)/(h)=
(12)/(13)

b=12

h=13

By using Pythagoras law

p=
√(13²-12²)=5

Now

exact values of tan θ=
(p)/(b)=
(5)/(12)

since it lies in II quadrant

tan θ=-
(5)/(12)

and

sinθ=
(p)/(h)=
(5)/(13)

since it lies in II quadrant

sin θ=
(5)/(13)

User Satake
by
7.9k points

Related questions

2 answers
0 votes
190k views
1 answer
4 votes
171k views
asked Feb 24, 2023 92.8k views
ILearner asked Feb 24, 2023
by ILearner
8.2k points
1 answer
5 votes
92.8k views