Find the values of s in the interval [0,pi/2] that make the statements true.
1. sin s=0.75438373
2. cos s=0.74241049
3. cot s=5.6394377
Can you tell me how you solve these.
You need either a calculator or a table of trig functions.
If you have a calculator, most have inverse trig functions, the yellow key and sin gives you the angle. The mode of the calculator can be set to work in degrees or radians.
for example
sin s=0.75438373
My TI-83 is in degree mode at present
yellow key sin
type
0.75438373
enter
48.97 degrees
to get radians without changing mode, now multiply that by pi/180
.8547147971 radians
by the way pi on this calculator is yellow key up arrow
Look, you need a calculator. Here is one.
For example for the angle whose sin is .75
type asin(.75) and click on the equal sign.
http://www.mathsisfun.com/scientific-calculator.html
Oh, by the way, asin is built in as a key so you can copy in your number and hit asin =
You can set the mode to radians or degrees on the upper right
However, I just bet your scientific calculator has arc sin (asin , sin^-1) and arc cos (acos, cos^-1) and arc tan
functions.
Get the manual out.
Well, solving these statements involves finding the values of s in the given interval that satisfy each equation. Let's go through them one by one, but keep in mind that I might throw in a little humor along the way!
1. sin s = 0.75438373
To solve this equation, we can use the inverse sine function (or arcsine). So, we can write it as s = sin^(-1)(0.75438373). You can use a calculator to find the inverse sine of 0.75438373, which is approximately 0.8588. But hey, remember to consider the interval [0,pi/2], so the value of s should be within that range. So, the value of s that makes this statement true is approximately 0.8588.
2. cos s = 0.74241049
To tackle this one, we can use the inverse cosine function (or arccosine). Let's write it as s = cos^(-1)(0.74241049). Use your handy calculator and you'll find that the inverse cosine of 0.74241049 is roughly 0.7464. However, keep in mind that we need s to be within the interval [0,pi/2]. So, the value that satisfies this statement is approximately 0.7464.
3. cot s = 5.6394377
Now, this one's a bit trickier. To solve for s, we'll use the inverse cotangent function (or arccotangent). So, we can write it as s = cot^(-1)(5.6394377). Now, my dear friend, let's grab that calculator again and find the inverse cotangent of 5.6394377. The result turns out to be about 0.1768. Remember, though, we only want the values of s within the interval [0,pi/2]. Sadly, 0.1768 falls outside that range. So, there are no values of s within the given interval that satisfy this statement.
And there you have it! The values of s that make these statements true are approximately 0.8588 and 0.7464, respectively.
Certainly! To find the values of s in the interval [0, pi/2] that satisfy the given trigonometric equations, you can use inverse trigonometric functions. Here's how you can solve each equation:
1. sin(s) = 0.75438373:
To find the value of s, you can take the inverse sine (also known as arcsine) of both sides of the equation:
s = arcsin(0.75438373)
Using a calculator, you can find that arcsin(0.75438373) is approximately 0.87418959. However, note that this value is in radians. Since you are looking for values in the interval [0, pi/2], the solution within this interval is approximately s = 0.87418959.
2. cos(s) = 0.74241049:
Similarly, you can take the inverse cosine (also known as arccosine) of both sides of the equation:
s = arccos(0.74241049)
Using a calculator, you can find that arccos(0.74241049) is approximately 0.73670072. Again, since you are looking for values in the interval [0, pi/2], the solution within this interval is approximately s = 0.73670072.
3. cot(s) = 5.6394377:
To find the value of s, you can take the inverse cotangent (also known as arccotangent) of both sides of the equation:
s = arccot(5.6394377)
Using a calculator, you can find that arccot(5.6394377) is approximately 0.17764278. Since you are looking for values in the interval [0, pi/2], the solution within this interval is approximately s = 0.17764278.
So, the values of s in the interval [0, pi/2] that satisfy the given equations are:
1. s = 0.87418959 (approx.)
2. s = 0.73670072 (approx.)
3. s = 0.17764278 (approx.)
i don't see those keys on my scientific calculator. can you tell me what would be the answer for the other two.
thnks alot