How do you find the exact values of the six trigonometric function of #theta# if the terminal side of #theta# in the standard position contains the point (4,4)?
First identify this as a 454590 degree triangle. From there, the ratios can be found (see below):
We have a
454590 triangles have a ratio of sides of 1, 1,
We can now work out the trig ratios:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the exact values of the six trigonometric functions of ( \theta ) when the terminal side of ( \theta ) in the standard position contains the point ( (4, 4) ), follow these steps:

Identify the Radius: Use the distance formula ( r = \sqrt{x^2 + y^2} ) to find the radius, where ( x = 4 ) and ( y = 4 ).

Identify the Angle ( \theta ): Use the inverse tangent function to find ( \theta ) using ( \theta = \arctan\left(\frac{y}{x}\right) ).

Find the Trigonometric Functions:
 ( \sin(\theta) = \frac{y}{r} )
 ( \cos(\theta) = \frac{x}{r} )
 ( \tan(\theta) = \frac{y}{x} )
 ( \csc(\theta) = \frac{1}{\sin(\theta)} )
 ( \sec(\theta) = \frac{1}{\cos(\theta)} )
 ( \cot(\theta) = \frac{1}{\tan(\theta)} )
Plug in the values of ( x ), ( y ), and ( r ) obtained from steps 1 and 2 into the respective trigonometric function formulas to find the exact values.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you evaluate #cot((5pi)/6)#?
 A fire is spotted 29 degrees west of South. The fire is 58 km from the look out station. A fire fighting base is 62 km due west of the first station. How far is the fire from the fighting base?
 How do you find the third angle given 65°, 88°?
 A sailor was in a boat that was 250 feet from the bottom of a lighthouse. Looking at the top of the lighthouse, the angle of elevation is 60 degrees. How do you find the height of the lighthouse is the tangent of 60 degrees = 1.73?
 At 10 am on april 26, 2000, a building 300 feet high casts a shadow 50 feet long. What is the angle of the elevation of the sun?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7