Finding Value of trignometric functions, given angle

Chapter 3 Class 11 Trigonometric Functions (Term 2)
Concept wise

sin (–x) = – sin x

cos (–x) = cos x

Note: Sometimes, these identities are called opposite angle identities

Since

cos (–x) = cos x

i.e. value of cos remains same after –x,

it is called even function

Since

sin (–x) = – sin x

i.e. value of sin becomes negative after –x,

it is called odd function

Thus, it is called odd-even identities also

We need to remember only these two,

for tan, cot, cosec, sec we can find using these two.

Let’s see

#### tan

Now, since tan = sin/cos

tan (–x) = sin (–x)/cos (–x)

= – sin x/cos x

= – tan x

∴ tan (–x) = – tan x

#### sec

Now, since sec = 1/cos

sec (–x) = 1/cos (–x)

= 1/cos x

= sec x

∴ sec (–x) = sec x

#### cosec

Now, since cosec = 1/sin

cosec (–x) = 1/sin (–x)

= 1/(– sin x)

= – 1/sin x

= – cosec x

∴ cosec (–x) = – cosec x

#### cot

Now, since cot = 1/tan

cot (–x) = 1/tan (–x)

= 1/(– tan x)

= – 1/tan x

= – cot x

∴ cot (–x) = – cot x

### Transcript

sin (–x) = – sin x cos (–x) = cos x Note: Sometimes, these identities are called opposite angle identities Since cos (–x) = cos x i.e. value of cos remains same after –x, it is called even function Since sin (–x) = – sin x i.e. value of sin becomes negative after –x, it is called odd function Thus, it is called odd-even identities also We need to remember only these two, for tan, cot, cosec, sec we can find using these two. Let’s see tan Now, since tan = sin/cos tan (–x) = sin (–x)/cos (–x) = – sin x/cos x = – tan x ∴ tan (–x) = – tan x sec Now, since sec = 1/cos sec (–x) = 1/cos (–x) = 1/cos x = sec x ∴ sec (–x) = sec x cosec Now, since cosec = 1/sin cosec (–x) = 1/sin (–x) = 1/(– sin x) = – 1/sin x = – cosec x ∴ cosec (–x) = – cosec x cot Now, since cot = 1/tan cot (–x) = 1/tan (–x) = 1/(– tan x) = – 1/tan x = – cot x ∴ cot (–x) = – cot x 