(4) Find $$ \sin heta, \cos heta, an heta, \sec heta $$ and $$ \cot heta $$ (5) Find $$ \sin 2 heta, \cos 2 heta $$ and $$ an 2 heta $$ (6) Find $$ \sin \frac{ heta}{2}, \cos \frac{ heta}{2} $$ and $$ an \frac{ heta}{2} $$

Question

(4) Find $$ \sin 	heta, \cos 	heta, 	an 	heta, \sec 	heta $$ and $$ \cot 	heta $$ (5) Find $$ \sin 2 	heta, \cos 2 	heta $$ and $$ 	an 2 	heta $$ (6) Find $$ \sin \frac{	heta}{2}, \cos \frac{	heta}{2} $$ and $$ 	an \frac{	heta}{2} $$

Ellis Klein · Accepted Answer

To find trigonometric values, use the angle $$ 	heta $$ and apply the following formulas: - Sine: $$ \sin 	heta = \frac{	ext{opposite}}{	ext{hypotenuse}} $$ - Cosine: $$ \cos 	heta = \frac{	ext{adjacent}}{	ext{hypotenuse}} $$ - Tangent: $$ 	an 	heta = \frac{\sin 	heta}{\cos 	heta} $$ - Secant: $$ \sec 	heta = \frac{1}{\cos 	heta} $$ - Cotangent: $$ \cot 	heta = \frac{1}{	an 	heta} $$ For double angles, use: - $$ \sin 2	heta = 2 \sin 	heta \cos 	heta $$ - $$ \cos 2	heta = \cos^2 	heta - \sin^2 	heta $$ - $$ 	an 2	heta = \frac{2	an 	heta}{1 - 	an^2 	heta} $$ For half angles, use: - $$ \sin \frac{	heta}{2} = \sqrt{\frac{1 - \cos 	heta}{2}} $$ - $$ \cos \frac{	heta}{2} = \sqrt{\frac{1 + \cos 	heta}{2}} $$ - $$ 	an \frac{	heta}{2} = \frac{\sin 	heta}{1 + \cos 	heta} $$

(4) Find \( \sin \theta, \cos \theta, \tan \theta, \sec \theta \) and \( \cot \theta \) (5) Find \( \sin 2 \theta, \cos 2 \theta \) and \( \tan 2 \theta \) (6) Find \( \sin \frac{\theta}{2}, \cos \frac{\theta}{2} \) and \( \tan \frac{\theta}{2} \)

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(4) Find \( \sin \theta, \cos \theta, \tan \theta, \sec \theta \) and \( \cot \theta \) (5) Find \( \sin 2 \theta, \cos 2 \theta \) and \( \tan 2 \theta \) (6) Find \( \sin \frac{\theta}{2}, \cos \frac{\theta}{2} \) and \( \tan \frac{\theta}{2} \)

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