Given Cos (theta)= -1/sqrt(2) With (theta) E [pi/2

Anonymous

From: -
Posts: -
Votes: -
Given cos (theta)= -1/sqrt(2) with (theta) E [pi/2, pi], sketch the unit circle indicating the quadrant position of (theta). (Find without calculator) a) sin (theta) b) tan (theta) c) sec (theta)

 

Answer No.1

Anonymous

From: -
Posts: -
Votes: -
Let's use x in place of Theta. SQRT is short for Square Root Part 1 sin x = Sqrt (1-Cos^2 x) => sin x = sqrt( 1-4/9) = sqrt(5/4) Since x is in the 4th Quadrant Sin x is negative sin x = -(sqrt(5))/2 Part 2 csc x = 1/sin x => csc x = 1/(-2/3) = 3/2 You can't put csc directly in a Calculator, use sin and then inverse it (1/sinx) Part 3 Tan x = sin x/ cos x = (3/4)/sqrt(1-9/16) = 3/sqrt(7) in Quadrant 2, Tan is negative. Therefore Tan x = -3/sqrt(7) Part 4: Cot x = 1/Tanx = 3/sqrt(7) (The value is positive because in Quandrant 3 Tan, Cot are positive) Use the calculator like the one i mentioned for csc sin x = sqrt(1-cos^2x) = 0.913545 Tan x = sin x/ cosx = -(0.913545/0.40673664) = -2.246037 The quadrant is important because the +/- sign changes with the quadrant in which x lies. Quad 1 - All are positive Quad 2 - Sin, Csc are positive, rest negative Quad 3 - Tan, Cot are positive, rest negative Quad 4 - Cos, Sec are positive, rest negative

Answer No.2

Anonymous

From: -
Posts: -
Votes: -
Cos (theta)= -1/sqrt(2) -> θ = 3π/4 Thus: a) sinθ = 1/√2 b) tanθ = 1 c) secθ = -√2

Answer No.3

Anonymous

From: -
Posts: -
Votes: -
C) sec (theta)

Answer No.4

Tunç Barış Aktekin

From: US
Posts: 10
Votes: 10
B) tan (theta)

Your Comment/Solution

Post As: Anonymous [Change]
Enter