Quiz 1 Topics Notes

Radian

A unit of angle measurement where a full circle is equivalent to 2\pi radians.

Degree

A unit of angle measurement where a full circle is equivalent to 360^{\circ}.

Degrees to radians conversion formula

\theta_{\text{rad}} = \theta_{\text{deg}} \cdot \frac{\pi}{180}

Radians to degrees conversion formula

\theta_{\text{deg}} = \theta_{\text{rad}} \cdot \frac{180}{\pi}

Reciprocal identity for cosecant (\csc \theta)

\csc \theta = \frac{1}{\sin \theta}

Reciprocal identity for secant (\sec \theta)

\sec \theta = \frac{1}{\cos \theta}

Reciprocal identity for cotangent (\cot \theta)

\cot \theta = \frac{1}{\tan \theta}

Quotient identity for tangent (\tan \theta)

\tan \theta = \frac{\sin \theta}{\cos \theta}

Quotient identity for cotangent (\cot \theta)

\cot \theta = \frac{\cos \theta}{\sin \theta}

Core Pythagorean identity

\sin^2 \theta + \cos^2 \theta = 1

Pythagorean identity for tangent and secant

1 + \tan^2 \theta = \sec^2 \theta

Pythagorean identity for cotangent and cosecant

1 + \cot^2 \theta = \csc^2 \theta

Sine definition in a right triangle

\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}

Cosine definition in a right triangle

\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}

Tangent definition in a right triangle

\tan \theta = \frac{\text{opposite}}{\text{adjacent}}

Pythagorean theorem for finding hypotenuse

For a right triangle with legs 'a' and 'b', the hypotenuse 'c' is given by c = \sqrt{a^2 + b^2}