1. In the 3rd quadrant, tan(theta) is positive, as in the third quadrant, both x and y are negative, and thus, tan(theta) = Perpendicular/Base = -y/-x = y/x which is positive. cot(theta) is also positive as cot(theta) = 1/tan(theta)
2. In the 4th quadrant, cos(theta) is positive, as in the 4th quadrant, x is positive and y is negative, and thus, cos(theta) = Base/Hypotenuse = x/sqrt(x^2 + y^2) which is positive. sec(theta) is also positive as sec(theta) = 1/cot(theta)
3. In the 2nd quadrant, sin(theta) is positive, as in the 2nd quadrant, y is positive and x is negative, and thus, sin(theta) = Perpendicular/Hypotenuse = y/sqrt(x^2 + y^2) which is positive. cosec(theta) is also positive as cosec(theta) = 1/sin(theta)
4. tan(theta) is positive in 1st and 3rd quadrant, and sin(theta) is negative in 3rd and 4th quadrant.
Thus, theta lies in 3rd quadrant.
5. cos(theta) is negative in 2nd and 3rd quadrant, and sin(theta) is negative in 3rd and 4th quadrant.
Thus, theta lies in 3rd quadrant.
6. cos(theta) is positive in 1st and 4th quadrant, and sin(theta) is positive in 1st and 2nd quadrant.
Thus, theta lies in 1st quadrant.
Write the correct answer in the blank. 1. Which trigonometric function is positive in the third...
Write the correct answer in the blank. 1. Which trigonometric function is positive in the third quadrant? 2. Which trigonometric function is positive in the fourth quadrant? 3. Which trigonometric function is positive in the second quadrant? Determine in which quadrant would lie given the following information. 4. tan e > 0 and sine <0 5. cos 0 <0 and sin 0 <0 6. sin e > 0 and cos > 0 Answer the following questions using the given information....
Write the first trigonometric function in terms of the second for in the given quadrant. cos(8), sin(e); in Quadrant III cos(0) = Submit Answer
MATH 1560 Name IDENTITIES ASSIGNMENT #2 Given the following information, determine the following trigonometric function values in exact form. tan B = -1 sin ß is positive tan a is negative 1. cos(2B) 2. sin(28) cos(a+B) sin(a+B) erify the following identities.
Use the information given about the angle 8 to find the exact value of each trigonometric function tan = - 10, sin < 0 0 e e (a) sin (20) (b) cos (20) 2 (d) cos 2 (e) tan 20 (f) tan 2 (c) sin
2. Solve the given trigonometric equation using Pythagorian Identities, cos? 0 + sin? 0 = 1, 1+tan? 0 = sec, cot? 0+1 = csc 0. (a) 1 - 2 sin’x = cos r. (b) 4 sin’t - 5 sin x - 2 cos” x = 2. (c) 2 tang - 2 sec1+1= = tan”.
9. Write the given expression as a sin 2x 1-cos 2x single trigonometric function 10. Solve for x. 2cos'x-cos x 1 9. Write the given expression as a sin 2x 1-cos 2x single trigonometric function 10. Solve for x. 2cos'x-cos x 1
e tan 15° 12. Answer True or False for each of the following. If the statement is false, make ne necessary change(s) to produce a true statement: a. The angle 0 =is larger than 90°. b. sin 45° + cos 45º = 1 C. Trigonometric functions can only be undefined at quadrantal angles. d. sin(30) = 3 sin e e tan 45º = 3 f. The value of trigonometric ratios (sine, cosine, tangent) depend only on the size of ,...
el 37-40 Quadrant in which an Angle Lies Find the quadrant in which 0 lies from the information given. 37. sin 0 <0 and cos e o ( 38. tan <0 and sine < 0
(10 points) First, determine the quadrant for 2; then find x, y, and r; and finally, give all six trigonometric ratios for a given the following information: csc(0) = 1 and cos(0) < 0 e lives in quadrant • X= • y = 1. sin(O) = 2. cos(0) = 3. tan(O) = 4. sec(0) = 5. csc(0) = 6. cot(0) =
Question Completion Status: Use the given triangle to write angle 0 as a function of x.. 5 X+3 e Tan ( ) e Sin ) e= Sin e cos