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# Trigonometric Worksheet

Trigonometric worksheet
• 1. Differentiate the function f (x) where f (x) = 3 sin (x) - 4 sin (x)?
1. 3 sin (x) + 4 cos (x)
2. 3 cos (x) + 4 sin (x)
3. 2 sin (x) + 4 cos (x)
4. 5 sin (x) + 8 cos (x)
• 2. Differentiate the function f ( x ) = x 3 tan ( x )?
1. 2( x sec 2 x + 3 tan x )
2. x2 ( cosec 2 x + 3 tan x )
3. x2 ( sec x + 3 tan x )
4. x2 ( sec x + 3 tan2 x )
• 3. Differentiate the function y = cos ( x ) / [ 1 + sin ( x ) ]?
1. -1 / 1 + cos (x)
2. -1 / 1 + cosec (x)
3. -1 / 1 + tan (x)
4. -1 / 1 + sin (x)
• 4. Perform differentiation operation on function y = cosec x . cot x?
1. - cosec x ( cos 2 x + cot 2 x )
2. - cosec x ( sin 2 x + cot 2 x )
3. - cosec x ( cosec 2 x + cot 2 x )
4. - cosec x ( cos x + cot x )
• 5. If f ( x ) = sin 2 x / cos 2 x, then find f' ( x )?
1. 2 tan x . sec 2 x
2. 2 tan x . sec  x
3. 2 tan 2 x . sec 2 x
4. 2 tan 3 x . sec2 x
• 6. Perform integration operation on function ∫ sin 3x dx?
1. - 1 / 3 sin 3x + c
2. - 1 / 3 cos 3x + c
3. - 1 / 3 tan 3x + c
4. - 1 / 3 cot 3x + c
• 7. Find the result of the given integral ∫ sin 5 x dx?
1. - cos x + 2 / 3 cos 3 x – 1 / 5 cos 5 x + c
2. - sin x + 2 / 3 cos 3 x – 1 / 5 cos 5 x + c
3. - cos x + 2 / 3 cos 3 x – 1 / 5 sin 5 x + c
4. - cos x + 2 / 3 cot 3 x – 1 / 5 cos 5 x + c
• 8. Calculate the result of the integral ∫ sin 6 x . cos 3 x dx?
1. 1 / 7 sin  x – 1 / 9 sin 9 x + c
2. 1 / 7 sin 7 x – 1 / 9 sin  x + c
3. 1 / 7 sin  x – 1 / 9 sin  x + c
4. 1 / 7 sin 7 x – 1 / 9 sin 9 x + c
• 9. Find the result of integral ∫ cos 2 x / ( 1 + sin x ) dx?
1. x + sin x + c
2. x + cot x + c
3. x + cos x + c
4. x - cos x + c
• 10. Evaluate the integral ∫ tan 3 x dx ?
1. 1 / 2 tan x – ln | sec x | + c
2. 1 / 2 tan 2 x + c
3. 1 / 2  ln | sec x | + c
4. 1 / 2 tan 2 x – ln | sec x | + c
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