Page 5 - Lesson Note

37.4 × 3 37.4 × 3 × 7
r = = = 35.7cm
π 22

2. If cosx = − , x lies in the third quadrant, find the values of other five trigonometric

functions

Solution: since cosx = − we have secx = −

Now sin x + cos x = 1 ⇒ sin x = 1 − cos x

⇒sin x = 1 − = ⇒ sinx = ±

Since x lies in the third quadrant sinx is negative. Therefore sinx = −

⇒ cosecx =−

Further tanx = = ⇒ cotx =

3. Find the value of sin50 − sin70 + sin10

Solution: sin50 − sin70 + sin10 = 2 cos sin + sin10

= −2cos60 sin10 + sin10 = 0

4. Prove that tan3xtan2xtanx = tan3x − tan2x − tanx
Proof: we know that 3x = 2x + x
∴ tan 3x = tan (2x + x)

⇒tan3x =

⇒tan3x − tan3xtan2xtanx = tan2x + tanx
⇒tan3x − tan2x − tanx = tan3xtan2xtanx
√
5. Find the solution of sinx = −

√
Solution: sinx = − = −sin = sin π + = sin

⇒ sinx = sin which gives

x = nπ + (−1) , n ∈ Z

6. Solve: sin2x − sin4x + sin6x = 0
Solution: The equation can be written as
sin6x + sin2x − sin4x = 0
⇒ 2sin4xcos2x − sin4x = 0
⇒sin4x(2cos2x − 1) = 0

∴ sin4x = 0 or cos2x =

∴ sin4x = 0 or cos2x = cos

Hence 4x = nπ or 2x = 2nπ ± , n ∈ z

⇒x = or x = nπ ± , n ∈ z