Your Progress 0 / 25 attempted
Q 01 / 25
The sine of an acute angle is always positive.
Q 02 / 25
\(\cos 0^\circ = 0\).
Q 03 / 25
The value of \(\tan 45^\circ\) is equal to 1.
Q 04 / 25
\(\sin 30^\circ = \cos 60^\circ\).
Q 05 / 25
The value of \(\sec \theta\) is undefined when \(\cos \theta = 0\).
Q 06 / 25
\(\sin(-\theta) = \sin\theta\).
Q 07 / 25
\(\cos(-\theta)=\cos\theta\).
Q 08 / 25
\(\tan\theta = \frac{\sin\theta}{\cos\theta}\) for all real \(\theta\).
Q 09 / 25
The period of \(\sin x\) is \(2\pi\).
Q 10 / 25
\(\sin(\pi-\theta)=\sin\theta\).
Q 11 / 25
\(\cos(\pi-\theta)=-\cos\theta\).
Q 12 / 25
\(\tan(\pi+\theta)=\tan\theta\).
Q 13 / 25
\(\sin^2\theta+\cos^2\theta=1\) holds for all real \(\theta\).
Q 14 / 25
\(\text{cosec}^2\,\theta-\cot^2\theta=1\).
Q 15 / 25
\(\sec^2\theta-\tan^2\theta=1\).
Q 16 / 25
\(\sin 2\theta = 2\sin\theta\cos\theta\).
Q 17 / 25
\(\cos 2\theta = 1-2\sin^2\theta\) is an identity.
Q 18 / 25
\(\tan 2\theta = \frac{2\tan\theta}{1-\tan^2\theta}\) for all \(\theta\).
Q 19 / 25
The domain of \(\tan x\) excludes odd multiples of \(\frac{\pi}{2}\).
Q 20 / 25
\(\sin x\) is a one–one function on \([0,2\pi]\).
Q 21 / 25
The principal value of \(\sin^{-1}x\) lies in \(\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\).
Q 22 / 25
\(\cos^{-1}(-x)=\pi-\cos^{-1}x) for (x\in[-1,1]\).
Q 23 / 25
\(\tan^{-1}x\) is defined for all real \(x\).
Q 24 / 25
If \(\sin\theta=\frac{3}{5}\) and \(\theta\) lies in the first quadrant, then \(\cos\theta=\frac{4}{5}\).
Q 25 / 25
The function \(f(x)=\sin x\) is invertible over \(\mathbb{R}\).

Frequently Asked Questions

Trigonometrical functions are functions that relate an angle to ratios of sides of a right-angled triangle or to coordinates on the unit circle

Because each angle corresponds to a unique real value of sine, cosine, tangent, etc

An angle measured in radians can take any real value, positive or negative

Radian is the angle subtended at the center of a circle by an arc equal in length to the radius

There are p radians in 180 degrees

The domain of sin x and cos x is all real numbers

The range is from -1 to 1 inclusive

All real numbers except odd multiples of \(\pi/2\)

Periodicity means the function repeats its values after a fixed interval

The period is \(2\pi\)

The period is \(\pi)

Identities that hold true for all permissible values of \(x\), such as \(\sin^2 x + \cos^2 x = 1\)

Identities that relate trigonometric functions as reciprocals of each other

Identities expressing tan x and cot x as ratios of sine and cosine

Identities derived from the Pythagorean theorem involving sin, cos, and tan
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