Question

Help Me!

Answer 1

Given the quadrant of theta in standard position and a trigonometric function value of theta , find the exact value for the indicated function.

II, sin theta = 0.4; sec theta

Answer 2

sec= 1/sin

Answer 3

@ZeHanz Please Help!

Answer 4

is there a multiple choice or just this??

Answer 5

Well since your not saying anything I will tell you what I think.............

sin is:
sin = opposite side/hypothenuse
right????!!!!!!

so then if sin was 45 then it would be:
Sin 45: =0.7071
(45 = 1/√2)

so in your case I would think that the answer would be: sin 158.9 (degrees)

Answer 6

did that help??

Answer 7

okay well I am not going to sit around for so long...so i hope what I did helped you!! and you have a good day :)

Answer 8

Sorry, that was what I was thinking but It didn't give an answer from my list of options. Thanks though! And in case you were wondering the answer was -5√21/21

Answer 9

ooo sry but you don't have to give me a medal...lol!! bc I got it wrong....

Answer 10

Hi @RobZBHayes, here's a unit circle with the possibilities for sin theta = 0.4.
As you can see, there are two angles, theta1 and theta2.
Now, you have to calculate sec theta.
Because sec theta = 1/ cos theta, you have to know the vaslue of cos theta.
We only have sin theta = 0.4, and the values for theta (see image) are not exactly known.
The good news is: you don't need theta at all!

You undoubtedly know this formula: sin²θ+cos²θ=1.
This means: cos²θ=1-sin²θ.=1-(0.4)²=1-0.16=0.84.

The only tricky part is: cos θ can have two values: plus or minus the square root of 0.84.
This means there are also two possibilities for sec θ = 1/cos θ.
Because there is no additional information about θ, we have to give them both.

To be more specific:\[\cos θ =\pm \sqrt{0.84}=\pm \sqrt{\frac{84}{100}}=\pm \frac{ 2\sqrt{21} }{ 10? }=\pm \frac{ \sqrt{21} }{ 5 }\]This means:\[\sec θ = \frac{ 1 }{ \cos θ }=\pm \frac{ 5 }{ \sqrt{21} }=\pm \frac{ 5 }{ 21 }\sqrt{21}\]