2 if cos14 and is in the 4th quadrant find the exact value for sin sin 3if sin13 and is in the 1

Step 1: For the first question, we are given that cos(θ) = 1/4 and θ is in the 4th quadrant. We

2 if cos14 and is in the 4th quadrant find the exact value...

2. If cos(θ)=1/4 and θ is in the 4th quadrant, find the exact value for sin(θ). sin(θ)= 3. If sin(θ)=1/3 and θ is in the 1st quadrant, find cos(θ) cos(θ) = Enter your answer as a reduced radical. 4. If θ=−11π / 6, then sin(θ) = cos(θ) = Give exact values.

Transcript

00:01 Given that cosine of theta equals one -fourth, and that theta falls in quadrant four, and we want to find sign of theta.

00:10 So first thing you want to do is recognize that cosine, and we're talking about something that's not necessarily on the unit circle, a theta value that's not necessarily on the unit circle.

00:23 Cosine stands for x over r, x being the x value of a point, r being the value of the radius.

00:33 So what we want to do is draw that angle of data on a coordinate plane with an x and a y axis.

00:45 What we know is that theta falls in quadrant four.

00:50 So our initial side will be the positive x -axis and that angle will go all the way around until quadrant four.

00:59 And we're not drawing an exact terminal side here.

01:03 It could be anywhere in quadrant four.

01:07 And what we know is that we have a circle here and the terminal side intersects that circle at a point, a point that has an x value and a y value.

01:21 And from the center of the circle out to that point, there is a radius.

01:26 We know from cosine being one -fourth that that radius is 4 and that x value is 1.

01:35 What that leaves us to find is the value of y.

01:38 And to find that, we can use the equation of a circle.

01:42 X squared plus y squared equals r squared.

01:46 Our x value is 1.

01:48 Our y value we don't know.

01:51 And our r value is 4.

01:56 1 squared is 1.

01:57 Y squared stays y squared.

02:01 4 squared is 16.

02:03 Subtract over that 1 and y squared is 15.

02:07 We take the square root.

02:09 And y could be either positive, or negative square root of 15.

02:14 Based off of its location on the unit circle has a positive x value, why should be negative? because we are in quadrant 4.

02:26 This allows us to solve for sine.

02:29 Just like cosine is x over r, sine is y over r.

02:34 So since we found our y value, and we already knew our r value, our final answer to this problem would be that sine of theta is negative radical 15 over 4.

02:54 In this next one, we have that sign of theta equals one -third, and theta falls in quadrant 1, and we want to find cosine of theta...

Question

2. If cos(θ)=1/4 and θ is in the 4th quadrant, find the exact value for sin(θ). sin(θ)= 3. If sin(θ)=1/3 and θ is in the 1st quadrant, find cos(θ) cos(θ) = Enter your answer as a reduced radical. 4. If θ=−11π / 6, then sin(θ) = cos(θ) = Give exact values.

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