TRIGONOMETRY WORKSHEET FOR GRADE 11

Trigonometry Worksheet for Grade 11 :

Here we are going to see some practice questions on trigonometry.

Worksheet - Problems and Solutions

(1)  Identify the quadrant in which an angle of each given measure lies

(i) 25 (ii) 825 (iii) −55 (iv) 328 (v) −230◦

Solution

(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

Solution

(3)  If a cos θ − b sin θ = c, show that a sin θ + b cos θ = ± √a2 + b2 − c2

(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

(7) 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)= 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 After having gone through the stuff given above, we hope that the students would have understood how to solve higher grade trigonometry problems.

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