Test: Basic Trigonometric Formulas - JEE MCQ

Step-by-step explanation:

• All three of them are positive in Quadrant I
• Sine only is positive in Quadrant II
• Tangent only is positive in Quadrant III
• Cosine only is positive in Quadrant IV
• 

Just look at the graph of cosine.

We know , Range of a function is the set of all possible outputs for that function. If you look at any 2π interval, the cosine function is periodic after every 2π.  as you can see it value range between -1 to 1 along the y-axis . So the range for cos function is [-1,1]

Sin 7π = Sin 7*180 = Sin 2π * 7  = 0
# Remember Sin nπ =0

√2 cannot be the value for Cosθ.

The values of  Cos θ at different angles are given below : 

Cos0°=1

Cos30°=√3/2

Cos45°=1/√2

Cos60°=1/2

Cos90°=0

The sign of the sinA and tanA in third quadrant is negative and positive.

tanx = -5/12
Therefore perpendicular = -5, base = 12
Applying pythagoras theorem,
(hyp)2 = (per)2 + (base)2
⇒ (-5)2 + (12)2
hyp = [25+144]1/2
hyp = (169)1/2
hyp = 13
sinx = perpendicular/hypotenous
= -5/13 
In second quadrant, only sin x, cosec x are positive
So. sinx = 5/13

In quadrant sin, cos tan, cot, sec, cosec all +ve .In second quadrant sin and cosec are +ve. in 3rd quadrant tan and cot are positive.And in 4th cos and sec are +ve.

Option C is not a trigonometric identity.