Exact Values of Trigonometric Functions - Questions With Answers
Find exact values of trigonometric functions without using a calculator. Questions with solutions and answers are presented. The trigonometric identities and formulas in this site may be used to solve the questions below.
Let us assume that we want to find the exact value of f(x), where f is any of the six trigonometric functions sine, cosine, tangent, cotangent, secant and cosecant. To find the exact value of f(x), we suggest the following steps:
1 - If the angle x is negative, we first use a formula for negative angles such as sin (- x) = - sin (x), cos (- x) = cos (x) and so on. 2 - Next we locate the terminal side of the angle in question, directly or using a positive coterminal angle t, which gives the sign of the trigonometric function. 3 - We find the reference angle Tr to the angle in question and use that fact that f(x) = + or - f(Tr). The sign + or - is determined using the quadrant found in step 2. If the angle in question or its coterminal angle are in quadrant 1, this last step is not needed.
Question 1Find the exact value of sin (- Pi / 3). Solution to Question 1:
Question 2Find the exact value of cos (- 390 ^{o}). Solution to Question 2:
Question 3Find the exact value of sec (3 Pi / 4). Solution to Question 3:
Question 4Find the exact value of cot ( 840 ^{o}). Solution to Question 4:
Question 5Find the exact value of csc (- 7 Pi / 4). Solution to Question 5:
Question 6Find the exact value of cot (121 Pi / 3). Solution to Question 6:
Question 7Find the exact value of sec ( - 3810 ^{o}). Solution to Question 7:
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