Trigonometric function values of quadrantal angles

In summary, there is no solution for 7 cot 270° + 4 csc 90° because tan(270°) is undefined and entering 7*cos(270°)/sin(270°) into a calculator will give a domain error.
  • #1
bgb
1
0
I can't seem to solve 7 cot 270° + 4 csc 90°
I don't know whether I'm entering something in my calculator wrong (could've sworn I was doing it right earlier) or if there just isn't an answer.

In my calculator, I enter 7/tan(270°)+4/sin(90°) and it gives me a domain error.
 
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  • #2
bgb said:
I can't seem to solve 7 cot 270° + 4 csc 90°
I don't know whether I'm entering something in my calculator wrong (could've sworn I was doing it right earlier) or if there just isn't an answer.

In my calculator, I enter 7/tan(270°)+4/sin(90°) and it gives me a domain error.

The reason is because tan(270°) is undefined.

You really shouldn't need a calculator for this, but if you really do, try entering as 7*cos(270°)/sin(270°).
 

FAQ: Trigonometric function values of quadrantal angles

What are quadrantal angles?

Quadrantal angles are angles that measure exactly 90 degrees, or a quarter of a full circle. These angles are commonly found in the four quadrants of the Cartesian coordinate system.

What are the trigonometric function values for quadrantal angles?

The trigonometric function values for quadrantal angles are as follows:

  • Sine (sin): 1 or -1
  • Cosine (cos): 0
  • Tangent (tan): Undefined or 0
  • Cosecant (csc): Undefined or 1 or -1
  • Secant (sec): Undefined or Infinity or -Infinity
  • Cotangent (cot): Undefined or 0

Why are some trigonometric function values undefined for quadrantal angles?

This is because the trigonometric functions are based on ratios of sides in a right triangle. In quadrantal angles, these ratios are undefined because one or more sides have a length of 0.

How can I remember the trigonometric function values for quadrantal angles?

A helpful mnemonic for remembering the function values is "SOH-CAH-TOA", which stands for "Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, and Tangent is Opposite over Adjacent". For quadrantal angles, Sine is always 1 or -1, Cosine is always 0, and Tangent is either undefined or 0.

How are quadrantal angles used in real life?

Quadrantal angles have various applications in fields such as engineering, physics, and navigation. For example, in engineering, quadrantal angles are used to calculate forces and moments in structures. In physics, these angles are used to analyze the motion of objects in circular motion. In navigation, quadrantal angles are used to determine the direction and distance of objects from a fixed point.

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