Search problems 5 problems match “Pythagorean identity”. Clear
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Trig expression with complementary angles ●○○○○ 10 ptsWithout using trigonometric tables, evaluate cos 2 26 ∘ + cos 64 ∘ sin 26 ∘ + tan 36 ∘ cot 54 ∘ \cos^2 26^\circ + \cos 64^\circ \sin 26^\circ + \dfrac{\tan 36^\circ}{\cot 54^\circ} cos 2 2 6 ∘ + cos 6 4 ∘ sin 2 6 ∘ + cot 5 4 ∘ tan 3 6 ∘ Trig expression with complementary angles ●○○○○ 10 ptsWithout using trigonometric tables, evaluate sin 2 34 ∘ + sin 2 56 ∘ + 2 tan 18 ∘ tan 72 ∘ − cot 2 30 ∘ \sin^2 34^\circ + \sin^2 56^\circ + 2\tan 18^\circ \tan 72^\circ - \cot^2 30^\circ sin 2 3 4 ∘ + sin 2 5 6 ∘ + 2 tan 1 8 ∘ tan 7 2 ∘ − cot 2 3 0 ∘ Trigonometric identities with complementary angles ●●○○○ 20 ptsEvaluate ( cos 2 25 ∘ + cos 2 65 ∘ ) + csc θ sec ( 90 ∘ − θ ) − cot θ tan ( 90 ∘ − θ ) (\cos^2 25^\circ + \cos^2 65^\circ) + \csc\theta \sec(90^\circ - \theta) - \cot\theta \tan(90^\circ - \theta) ( cos 2 2 5 ∘ + cos 2 6 5 ∘ ) + csc θ sec ( 9 0 ∘ − θ ) − cot θ tan ( 9 0 ∘ − θ ) Sine of a double angle from a shifted sine ●●○○○ 20 ptsGiven α ∈ ( 0 , π 2 ) \alpha \in (0, \frac{\pi}{2}) α ∈ ( 0 , 2 π ) sin ( 2 α − π 3 ) = 3 3 \sin (2\alpha - \frac{\pi}{3}) = \frac{\sqrt{3}}{3} sin ( 2 α − 3 π ) = 3 3 sin 2 α \sin 2\alpha sin 2 α Sine of a difference from given values ●●●○○ 50 ptsGiven that α , β ∈ ( π 3 , 5 π 6 ) \alpha, \beta \in \left(\frac{\pi}{3}, \frac{5\pi}{6}\right) α , β ∈ ( 3 π , 6 5 π ) sin ( α + π 6 ) = 4 5 \sin\left(\alpha + \frac{\pi}{6}\right) = \frac{4}{5} sin ( α + 6 π ) = 5 4 cos ( β − 5 π 6 ) = 5 13 \cos\left(\beta - \frac{5\pi}{6}\right) = \frac{5}{13} cos ( β − 6 5 π ) = 13 5 sin ( α − β ) \sin(\alpha - \beta) sin ( α − β )