If tan θ = 1/ 8 and cot ϕ = 9/10 , find the exact value of sin ( θ − ϕ ).

Answer 1

Will use a and b . To find sin (a-b) we first have to calculate sine and cosine values for the 2 angles using right angle trig

sin(a)= 1/sqroot 65

sin(b)= 10/sqroot 181

cos(a)= 8/sqroot 65

cos(b)= 9/sqroot 181

sin(a-b)= sin(a)cos(b)-sin(b)cos(a). We have these values and can plug them in

1/(sqroot 65)(9)/sqroot 181 - 10/sqroot 65(8)/sqroot 181= 9/sqroot11765 - 80/sqroot 11765=

-71/sqroot 11765= -.654

Answer 2

Use Pythagoras to determine these values!

tan θ = 1/8, sin θ = √17 / 17, cos θ = 8√17 / 17

cot φ = 9/10, sin φ = 10√81 / 81, cos φ = 9√81 / 81

sin (θ + φ) = sin θ cos φ + cos θ sin φ This is a sum formula - should be in you text book.

Can you substitute values and answer?

Answer 3

sin(a - b) = sin a cos b - cos a sin b

Use Pythagorean theorem to get sin a=8/sqrt(65) cos a = 1/sqrt(65) sin b = 9/sqrt(181) and

cos b = 10/sqrt(181)

Then plug in the values to get your answer.

Note: I used a and b rather than the Greek letters.