Trigonometric Quadrants- Test Questions-i

Question 11

Question:   Find cos q if

Answer:   

Question 12

Question:  
(i) sin (x + y) (ii) sin (x - y) (iii) cos (x + y) (iv) cos (x - y).

Answer:   






(ii) sin (x - y) = sin x cos y - cos x sin y


(iii) cos (x + y) = cos x cos y - sin x sin y


(iv) cos (x - y) = cos x cos y + sin x sin y

Question 13

Question:  
(i) cos (x - y)
(ii) sin (x + y)

Answer:   
Both sin x and cos x are positive as x lies in I quadrant.

Both cos y and sin y are positive as y lies in I quadrant.
i) cos (x - y) = cos x cos y + sin x sin y


ii) sin (x + y) = sin x cos y + cos x sin y

Question 14

Question:   Find x, if

Answer:   
cos x is negative in both II and III quadrants.




cos x lies in III quadrant only.


positive in I and IV quadrants.

Question 15

Question:  
(i) cos (a + b) (ii) sin (a - b) (iii) sin (a + b) (iv)cos (a - b).

Answer:   






(i) cos (a + b) = coa a cos b - sin a sin b


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



iii) sin (a + b) = sin a cos b + cos a sin b


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

Question 16

Question:  

Answer:   











sin(q+f) = sinq cosf + cosq sinf


Since sin (q + f) and cos (q + f) are both positive, (q + f) lies in the I quadrant.

Question 17

Question:   in the first quadrant. Find sin A.

Answer:   

Question 18

Question:  

Answer:   

Question 19

Question:   Prove that

Answer:   

Question 20

Question:   Prove that

Answer: