The values of the six trigonometric functions for angle A are:
sin(A) = [tex]\frac{\sqrt{2}}{2}[/tex] and csc(A) = [tex]\sqrt{2}[/tex]
cos(A) = [tex]-\frac{\sqrt{2}}{2}[/tex] and sec(A) = [tex]-\sqrt{2}[/tex]
tan(A) = - 1 and cot(A) = - 1
Step-by-step explanation:
Let us revise the sign of the six trigonometry functions in each quadrant
1. In the first quadrant all the trigonometry functions of Ф are positive
2. In the second quadrant sin(Ф) and csc(Ф) only are positive
3. In the third quadrant tan(Ф) and cot(Ф) only are positive
4. In the fourth quadrant cos(Ф) and sec(Ф) only are positive
The angle is positive when the terminal side of the angle rotates
counterclockwise from 1st quadrant to 4th quadrant
The angle is negative when the terminal side of the angle rotates
clockwise from 4th quadrant to 1st quadrant
0° < Ф < 90° ⇒ 1st quadrant ⇒ -360° < Ф < -270°
90° < Ф < 180° ⇒ 2nd quadrant ⇒ -270° < Ф < -180°
180° < Ф < 270° ⇒ 3rd quadrant ⇒ -180° < Ф < -90°
270° < Ф < 360° ⇒ 4th quadrant ⇒ -90° < Ф < 0°
∵ m∠A = -225
∴ ∠A lies in the 2nd quadrant
∴ sin(A) , csc(A) are positive values and tan(A) , cot(A) , cos(A) ,
sec(A) are negative
∵ The positive equivalent angle of ∠A = 360° - 225° = 135°
∵ In the second quadrant 135° = 180° - 45°
∴ The positive acute angle equivalent to ∠A is 45°
∴ sin(A) = sin(45) ⇒ csc(A) = csc(45)
∴ cos(A) = - cos(45) ⇒ sec(A) = - sec(45)
∴ tan(A) = - tan(45) ⇒ cot(A) = - cot (45)
∵ sin(45) = [tex]\frac{\sqrt{2}}{2}[/tex] and csc(45) = [tex]\sqrt{2}[/tex]
∵ cos(45) = [tex]\frac{\sqrt{2}}{2}[/tex] and sec(45) = [tex]\sqrt{2}[/tex]
∵ tan(45) = 1 and cot(45) = 1
∴ sin(A) = [tex]\frac{\sqrt{2}}{2}[/tex] and csc(A) = [tex]\sqrt{2}[/tex]
∴ cos(A) = [tex]-\frac{\sqrt{2}}{2}[/tex] and sec(A) = [tex]-\sqrt{2}[/tex]
∴ tan(A) = - 1 and cot(A) = - 1
The values of the six trigonometric functions for angle A are:
sin(A) = [tex]\frac{\sqrt{2}}{2}[/tex] and csc(A) = [tex]\sqrt{2}[/tex]
cos(A) = [tex]-\frac{\sqrt{2}}{2}[/tex] and sec(A) = [tex]-\sqrt{2}[/tex]
tan(A) = - 1 and cot(A) = - 1
Learn more;
You can learn more about trigonometry functions in brainly.com/question/4924817
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