West Texas A&M UniversityTrigonometric Equations Questions Response More practice and directions are in the attatched file. Practice Problem #1) 16 Sinx –

West Texas A&M UniversityTrigonometric Equations Questions Response More practice and directions are in the attatched file.

Practice Problem #1) 16 Sinx – 4 = 0; x [0,2?]

Explanation #1

Step 1) 4(cosx+1) = 2

4 Cosx + 4 = 2

4 Cosx = 2 – 4

4 Cosx = -2

Cosx = -2/4

Cosx = -1/2

Step 2) Cos is negative and as a result found in Quadrant II and Quadrant III.

A cos value of -1/2 is a reference angle of 600.

This is considered the reference angle of 600 quadrants II and III.

x = 1200 and 2400 or 2?/3 and 4?/3

Answer = 1200 and 2400

Practice Problem #2) 16 Sinx – 4 = 0; x[0,2?] Fstfinalexamreview.wikispaces.com
Examples:
Solve sin(?x?) + 2 = 3 over the interval 0?0? ? ?x? < 360?0 Just as with ?linear equations?, I'll first isolate the variable containing term: sin(?x?) + 2 = 3 sin(?x?) = 1 Now I'll use the reference angles I've memorized to get my final answer. Note: The instructions gave me the interval in terms of degrees, which means that I'm supposed to give my answer in degrees. Yes, the sine, on the first period, takes on the value of 1 at ? radians, but that's not the angle-measure type they're wanting, and using this as my answer would probably result in my at least losing a few points on this question. So, in degrees, my answer is: ?x? = 90?0 http://www.purplemath.com/modules/solvtrig.htm Example: ?Solve: 2 cos?x? - 1 = 0; ?x?[0,2?] Explanation Step 1) 2 Cos?x? - 1 = 0 2 Cos?x? = 1 Cos?x? = 1/2 Step 2) Now, Cos is positive in Quadrant I and Quadrant IV. Also, a Cos value of 1/2 is a reference angle of 60?0?. Consider the reference angle of 60?0? in quadrants I and II. x? = 60?0? and 300?0? or ?/3 and 5?/3 Answer = ? ? ?x? = 60?0? and 300?0.? Practice Problem #1)? ?16 Sin?x? - 4 = 0; ?x? [0,2?] Explanation #1 Step 1) 4(cos?x?+1) = 2 4 Cos?x? + 4 = 2 4 Cos?x? = 2 – 4 4 Cos?x? = -2 Cos?x? = -2/4 Cos?x? = -1/2 Step 2) Cos is negative and as a result found in Quadrant II and Quadrant III. A cos value of -1/2 is a reference angle of 60?0?. This is considered the reference angle of 60?0? quadrants II and III. x? = 120?0? and 240?0? ?or? 2?/3 and 4?/3 Answer =? ?120?0? ?and ?240?0 Practice Problem? #2)? 16 Sin?x? - 4 = 0; ?x?[0,2?] Explanation #2 Step 1) 16Sin?x? - 4 = 0 16Sin?x? = 4 Sin?x? = 4/16 Sin?x? = 1/4 Step 2) Sine is positive in Quadrant I and Quadrant II. Also, a sine value of 1/4 is a reference angle of 45?0?. This is considered the reference angle of 45?0? quadrants I and II. x= ? 45?0? and 135?0? or ?/4 and 3?/4 Answer = ?45?0? and 135?0 Practice Problem? ?#3)? ?2tan?x? - 2 = 0: ?x?[0,2 ?] Explanation #3 Step 1) 2tan?x? - 2 = 0 2tan?x? = 2 tan?x? = 2/2 tan?x? = 1 Step 2) Now, tan is positive in the Quadrant I and Quadrant III. A tan value of 1 is a reference angle of 45?0?. This is considered the reference angle of 45?0? quadrants I and III. x? = 45?0? and 225?0? or ?/4 and 5?/4 Answer =? ?45?0? ?and? 225?0 Review Directions: Solve each of the following problems. Purchase answer to see full attachment