All Precalculus ResourcesSolve the following: Correct answer: Explanation: Rewrite in terms of sine and cosine functions. Since these angles are special angles from the unit circle, the values of each term can be determined from the x and y coordinate points at the specified angle. Solve each term and simplify the expression. Find the value of . Correct answer: Explanation: Using trigonometric relationships, one can set up the equation . Solving for , Thus, the answer is found to be 29. Find the value of . Correct answer: Explanation: Using trigonometric relationships, one can set up the equation . Plugging in the values given in the picture we get the equation, . Solving for , . Thus, the answer is found to be 106. Find all of the angles that satistfy the following equation: Correct answer: OR Explanation: The values of that fit this equation would be: and because these angles are in QI and QII where sin is positive and where . This is why the answer is incorrect, because it includes inputs that provide negative values such as: Thus the answer would be each multiple of and , which would provide the following equations: OR Evaluate: Correct answer: Explanation: To evaluate , break up each term into 3 parts and evaluate each term individually. Simplify by combining the three terms.
What is the value of ? Correct answer: Explanation: Convert in terms of sine and cosine. Since theta is radians, the value of is the y-value of the point on the unit circle at radians, and the value of corresponds to the x-value at that angle. The point on the unit circle at radians is . Therefore, and . Substitute these values and solve. Solve: Correct answer: Explanation: First, solve the value of . On the unit circle, the coordinate at radians is . The sine value is the y-value, which is . Substitute this value back into the original problem. Rationalize the denominator. Find the exact answer for: Correct answer: Explanation: To evaluate , solve each term individually. refers to the x-value of the coordinate at 60 degrees from the origin. The x-value of this special angle is . refers to the y-value of the coordinate at 30 degrees. The y-value of this special angle is . refers to the x-value of the coordinate at 30 degrees. The x-value is . Combine the terms to solve . Find the value of . Correct answer: Explanation: The value of refers to the y-value of the coordinate that is located in the fourth quadrant. This angle is also from the origin. Therefore, we are evaluating . Simplify the following expression: Correct answer: Explanation: Simplify the following expression: Begin by locating the angle on the unit circle. -270 should lie on the same location as 90. We get there by starting at 0 and rotating clockwise So, we know that And since we know that sin refers to y-values, we know that So therefore, our answer must be 1 All Precalculus ResourcesWhat are the 6 trigonometric functions?There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
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