Trignometric Ratios, Functions and Equations Test - 2

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  2 π interval, the cosine function is periodic after every  2 π. 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 7 π= Sin 7*180 = Sin 2 π* 7  = 0
# Remember  Sin n π=0

√2 cannot be the value for Cos θ.

The values of   Cos θat 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.