inverse trig qns (1 Viewer)

[Masaken]

Question is essentially to find their exact values.

Need help with part (d) -- I know the related angle is pi/8, but what happens to the negative??, and for part (f) in where to start? thanks in advance

 

[Life'sHard]

(d) Use your understanding of trig quadrants. (f) from the looks of it you expand sin(pi + pi/3) then just tan inverse the result.

 

[Life'sHard]

View attachment 36165

I’m pretty sure the angles are pi/8 and 4pi/3

 

[Drongoski]

4pi/3 ??

-pi/2 < theta < pi/2

 

[cossine]

Question is essentially to find their exact values.
View attachment 36163
Need help with part (d) -- I know the related angle is pi/8, but what happens to the negative??, and for part (f) in where to start? thanks in advance

Remember year 9 math. ASTC

d) -cos (7pi/8) = cos(pi/8) . Now use the the theorem f^-1(f(x)) = x to get pi/8.

f) I presume can figure out the value -2sin(4pi/3). Now if you know the exact value of tan^-1(sqrt(3)) you will get the answer. Remember the special triangles i.e. {1, 1, sqrt(2)} and { 1, sqrt(3), 2}.

 

[cossine]

(d) Use your understanding of trig quadrants. (f) from the looks of it you expand sin(pi + pi/3) then just tan inverse the result.

Almost correct. Drogonski as already mention but it will make it clear. By definition the range of tan^-1 is "-pi/2 < theta < pi/2" so 4pi/3 is not valid answer.