Question

if sin theta is equal to 6 by 7 and theta is an acute angle find the other five trigonometric function values for theta​

Answer 1

Answer:

sine theta =p/h

=6/7

so, p=6 & h=7

b=√7^2-6^2

b=√13

cos theta=b/h

tan theta=p/b

cosec theta=h/p

sec theta=h/b

cot theta =b/p

put the value

Answer 2

Given:

sin theta 6/7 and theta is an acute angle

To find:

If sin theta 6/7 and theta is an acute angle find the other five trigonometric function values for theta

Solution:

From given, we have,

sin theta 6/7 and theta is an acute angle  

we know that sin theta is a ratio of the opposite side by the hypotenuse.

So, we have, have,

h² = o² + a²

7² = 6² + a²

49 - 36 = a²

∴ a = √13

Thus the adjacent side is √13.

The trigonometric ratios are:

cos theta = a/h = √13/7

tan theta = o/a = 6/√13

sec theta = h/a = 7/√13

coses theta = h/o = 7/6

cot theta = a/o = √13/7

Therefore, the other five trigonometric function values for theta are: cos theta = √13/7, tan theta = 6/√13, sec theta = 7/√13, coses theta = 7/6 and cot theta = √13/7