SOLUTION: Given that sin θ=3/4, and that θ is acute, find the value of
a) sec θ
b) cot θ
Algebra.Com
Question 552087: Given that sin θ=3/4, and that θ is acute, find the value of
a) sec θ
b) cot θ
Answer by neatmath(302) (Show Source): You can put this solution on YOUR website!
There is a lot to this subject, but let's see what we can do here.
The first thing to realize is that we are dealing with angles between 0 and pi/2, or between 0 and 90 degrees.
Okay, our first step is to draw an angle in Quadrant I.
It doesn't matter what the angle looks like, it just needs to be between 0 and pi/2.
Now, make a triangle out of the angle. Use the x-axis as one side of the triangle, and a line connecting the x-axis to the line of the angle you made to make the other side of the triangle.
Of course, the hypotenuse is formed by the angle you first constructed.
Now, you should have a basic right triangle.
Using our given information, lets see if we can find the values for all 3 sides of the triangle!
We have to remember our mnemonic of Soh Cah Toa, to find these values.
Since the sin is 3/4, we know that the "opposite" over the "hypotenuse" is 3 over 4.
Then, the vertical side of our triangle, the one opposite our constructed angle has a value of 3.
Our hypotenuse has a value of 4.
Now we can use the Pythagorean Theorem to find the value for the horizontal side, which we can call x:
or
Since we are in Quadrant I, we know that we must use the first positive value
Now, we just need to use our three values to find our answers!
sin is opposite/hypotenuse, that's where our value of 3/4 came from
cos is adjacent/hypotenuse, or
The sec is the reciprocal of the cos, so that would be
Of course we can rationalize this a bit,
Our tan would be opposite/adjacent or
So then of course, our cot, is the reciprocal of the tan.
Then the cot would be
So, there are a LOT of ways to find these answers. Tables, calculators, graphing utilities, and others.
But this is the simplest way, and you don't need any "tools" in order to solve for these values.
In addition, you are able to find the EXACT answers, something that "some" calculators can't even do.
Mine does, but I didn't even pick it up to solve this problem. :)
Like I said, there is a LOT to this subject, but this is a good start.
I hope this helps! :)
Email Scott: neatmath@yahoo.com for help with specific problems,
or to inquire about mathematics tutoring via email or other methods.
Paypal is always accepted for single problems or for more intensive tutoring!
Single problems would range from 50 cents to 5 dollars each, depending on the complexity.
RELATED QUESTIONS
find the value of √sinθ cosθ/secθ cscθ given that tanθ=3/4 (answered by Alan3354)
Find the value of √sinθ cosθ/secθ cscθ given that tanθ=3/4 (answered by Alan3354)
1). Find the length of an arc that subtends a central angle of 150 ° in a circle of... (answered by stanbon)
Use the appropriate reciprocal identity to find the function value of
a. cot θ,... (answered by solver91311)
9. Find the values of the six trigonometric functions of the acute angle in standard... (answered by Fombitz)
Find the values of the trigonometric functions of θ if csc θ = 13/9
and... (answered by Alan3354,ewatrrr)
If secθ= 4/3 and θ terminates in Quadrant IV, find the exact values for all six (answered by lwsshak3)
Given sec θ = - 5/4 and cosec θ = - 5/3 find sinθ cosθ tanθ and... (answered by Fombitz)
FInd the values of θ between 0° and 180° for which
a) secθ= cosecθ
b)... (answered by Theo)