Find the value of $\sin\left(\frac{5\pi}{36}\right)\cos\left(\frac{\pi}{36}\right)+\sin\left(\frac{\pi}{36}\right)\cos\left(\frac{5\pi}{36}\right)$sin(5π36)cos(π36)+sin(π36)cos(5π36) in exact form.

Easy

2min

Find the exact value of $\cos\frac{21\pi}{10}\cos\frac{\pi}{10}+\sin\frac{21\pi}{10}\sin\frac{\pi}{10}$cos21π10cosπ10+sin21π10sinπ10.

Easy

1min

Find the exact value of $\frac{\tan\frac{2\pi}{9}-\tan\frac{\pi}{18}}{1+\tan\frac{2\pi}{9}\tan\frac{\pi}{18}}$tan2π9−tanπ181+tan2π9tanπ18.

Easy

2min

Suppose $\cos A=\frac{3}{5}$cosA=35 and $\sin B=\frac{15}{17}$sinB=1517, where $00<A<π2 and $00<B<π2.

Easy

12min

Outcomes

11.SF.TF.1

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin^2 x + cos^2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities like following: cot(x + or - y), sin x + sin y, cos x + cos y, sin x - sin y, cos x - cos y (see syllabus document)

Evaluate trig expressions using angle sum and difference identities

Interactive practice questions

Outcomes

11.SF.TF.1

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