Trigonometry worksheet for grade 11 :
Here we are going to see some practice questions on trigonometry.
(1) Identify the quadrant in which an angle of each given measure lies
(i) 25◦ (ii) 825◦ (iii) −55◦ (iv) 328◦ (v) −230◦
(2) For each given angle, find a coterminal angle with measure of θ such that 0◦ ≤ θ < 360◦
(i) 395◦ (ii) 525◦ (iii) 1150◦ (iv) −270◦ (v) −450◦
(3) If a cos θ − b sin θ = c, show that a sin θ + b cos θ = ± √a2 + b2 − c2. Solution
(4) If sin θ + cos θ = m, show that cos6 θ + sin6 θ = 4 − 3 (m2 − 1)2/4, where m2 ≤ 2. Solution
(5) If (cos4 α/cos2 β) + (sin4 α/sin2 β) = 1, prove that
(i) sin4 α + sin4 β = 2sin2 α sin2 β
(ii) (cos4 β/cos2 α) + (sin4 β/sin2 α) = 1. Solution
(6) If y = 2 sinα/(1 + cos α + sinα), then prove that (1 − cos α + sinα)/(1 + sinα) = y. Solution
(8) If tan2 θ = 1 − k2, show that sec θ + tan3 θ cosec θ = (2−k2)3/2. Also, find the values of k for which this result holds. Solution
(9) If sec θ + tanθ = p, obtain the values of sec θ, tan θ and sin θ in terms of p Solution
(10) If cot θ (1 + sin θ) = 4m and cot θ (1 − sin θ) = 4n, then prove that (m2 − n2)2 = mn Solution
(11) If cosec θ − sin θ = a3 and sec θ − cos θ = b3, then prove that a2b2 (a2 + b2) = 1. Solution
(12) Eliminate θ from the equations a sec θ − c tan θ = b and bsec θ + d tan θ = c. Solution
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