Question

sin π+2cos π+3sin 3π/2+4 cos 3π/2 -5sec π -6cosec 3π/2 evaluate value​

Answer 1

Step-by-step explanation:

Here,

sin π + 2cos π + 3sin 3π/2 + 4 cos 3π/2 - 5sec π - 6cosec 3π/2

= 0 + 2×(-1) + 3×(-1) + 4×0 - 5×(-1) - 6×(-1)

= 0 - 2 - 3 + 0 + 5 + 6

= 11-5

= 6

Answer 2

Answer:

sin π +2 cos π + 3 sin $\frac{3\pi}{2}$ + 4 cos  $\frac{3\pi}{2}$ - 5 sec π - 6 cosec  $\frac{3\pi}{2}$ = 6

Step-by-step explanation:

Given: sin π +2 cos π + 3 sin $\frac{3\pi}{2}$ + 4 cos  $\frac{3\pi}{2}$ - 5 sec π - 6 cosec  $\frac{3\pi}{2}$

We know the values of standard angles,

Therefore, sin π = 0

                 cos π = - 1

                 sin $\frac{3\pi}{2}$  = - 1

                cos  $\frac{3\pi}{2}$ = 0

Therefore,

sin π +2 cos π + 3 sin $\frac{3\pi}{2}$ + 4 cos  $\frac{3\pi}{2}$ - 5 sec π - 6 cosec  $\frac{3\pi}{2}$

We know that sec $\theta$ = $\frac{1}{cos \theta}$

and cosec $\theta$ = $\frac{1}{sin \theta}$

= sin π +2 cos π + 3 sin $\frac{3\pi}{2}$ + 4 cos  $\frac{3\pi}{2}$ - 5 $\frac{1}{cos \pi}$ - 6 $\frac{1}{sin\frac{3\pi}{2}}$

Substituting the values, we get,

= 0 + 2 (-1) + 3 (-1) + 4 (0) - 5 $(\frac{1}{-1})$ - 6 $(\frac{1}{-1})$

= 0 - 2 - 3 + 0 + 5 + 6

= 6

Therefore,

sin π +2 cos π + 3 sin $\frac{3\pi}{2}$ + 4 cos  $\frac{3\pi}{2}$ - 5 sec π - 6 cosec  $\frac{3\pi}{2}$ = 6