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3. a find all the solutions between 2 and 2 of...

# Question: a find all the solutions between 2 and 2 of...

###### Question details

(a) Find all the solutions between −2π and 2π of the equation cos θ = − √ 3/ 2 , giving all your answers as exact values in radians. (b) In triangle ABC (with the usual notation), angle A = 29◦ , side b = 11 and side c = 8. (i) Use the cosine rule to find the length of side a, to two decimal places. (ii) Without using the cosine rule again, find the remaining angles B and C, giving your answers to the nearest degree.

(c)Using the exact values for the sine and cosine of both π/4 and π/6, and the angle difference identity for cosine, find the exact value of cos(π/12). (d) Use the exact value of cos(π/6) and the half-angle identity for sine to find the exact value of sin(π/12). (e) Use the standard trigonometric identity sin2 θ + cos2 θ = 1 to check the exact values you found in parts (c) and (d).

###### Solution by an expert tutor 