find the exact values of the six trig functions of the angle.
-750
sin(-750)=
cos(-750)=
tan(-750)=
csc(-750)=
sec(-750)=
cot(-750)=
I've tried this question over and over again and i cannot get it right. i believe -750 is in the fourth quadrant but I'm not sure. can someone solve this question for me. thanks!
oh and its in degrees.
nevermind, figured it out.
To find the exact values of the six trigonometric functions for an angle of -750 degrees, let's first find the corresponding positive angle in the range 0 to 360 degrees.
-750 + 360 = -390 degrees
Since -390 degrees is still in the fourth quadrant, we can use the following relationships for the trigonometric functions:
sin(-750) = -sin(390)
cos(-750) = cos(390)
tan(-750) = -tan(390)
csc(-750) = -csc(390)
sec(-750) = sec(390)
cot(-750) = -cot(390)
Now, let's find the exact values for each of these functions:
Using a calculator or reference table, we can find the values for sin(390), cos(390), and tan(390):
sin(390) ≈ 0.6428
cos(390) ≈ -0.7660
tan(390) ≈ -0.8391
Using the reciprocal identities, we can find the values for csc(390), sec(390), and cot(390):
csc(390) = 1 / sin(390) ≈ 1 / 0.6428 ≈ 1.5565
sec(390) = 1 / cos(390) ≈ 1 / (-0.7660) ≈ -1.3052
cot(390) = 1 / tan(390) ≈ 1 / (-0.8391) ≈ -1.1918
So, the exact values of the six trigonometric functions for an angle of -750 degrees are:
sin(-750) ≈ -sin(390) ≈ -0.6428
cos(-750) ≈ cos(390) ≈ -0.7660
tan(-750) ≈ -tan(390) ≈ 0.8391
csc(-750) ≈ -csc(390) ≈ -1.5565
sec(-750) ≈ sec(390) ≈ -1.3052
cot(-750) ≈ -cot(390) ≈ 1.1918
To find the values of the six trigonometric functions for the angle -750 degrees, we need to determine the equivalent angle within a full revolution or 360 degrees.
Since -750 degrees is greater than -360 degrees, we can subtract 360 degrees from -750 degrees until we obtain an angle within one full revolution.
-750 degrees - 360 degrees = -1110 degrees
-1110 degrees - 360 degrees = -1470 degrees
-1470 degrees - 360 degrees = -1830 degrees
Now we have an angle within one complete revolution, which is -1830 degrees.
To determine the values of the six trigonometric functions, we first need to find the reference angle. The reference angle is the acute angle formed between the terminal side of the angle and the x-axis.
To find the reference angle, we can use the formula: reference angle = |angle| mod 360
The absolute value of -1830 degrees is 1830 degrees.
1830 degrees mod 360 degrees = 90 degrees.
So, the reference angle is 90 degrees.
Now, based on the quadrant in which the angle falls, we can determine the sign of each trigonometric function:
Since -1830 degrees lies in the third quadrant (between 180 and 270 degrees), the signs are as follows:
Sine (sin): negative (sin(-1830) < 0)
Cosine (cos): negative (cos(-1830) < 0)
Tangent (tan): positive (tan(-1830) > 0)
Cosecant (csc): negative (csc(-1830) < 0)
Secant (sec): negative (sec(-1830) < 0)
Cotangent (cot): positive (cot(-1830) > 0)
Now we need to find the values of these trigonometric functions for the reference angle, which is 90 degrees:
Sine (sin(90)): sin(90) = 1
Cosine (cos(90)): cos(90) = 0
Tangent (tan(90)): tan(90) is undefined (since cos(90) = 0)
Cosecant (csc(90)): csc(90) = 1/sin(90) = 1/1 = 1
Secant (sec(90)): sec(90) = 1/cos(90) = 1/0 (undefined)
Cotangent (cot(90)): cot(90) = 1/tan(90) = 1/undefined (undefined)
So the exact values of the six trigonometric functions for the angle -750 degrees are:
sin(-750) = -sin(90) = -1
cos(-750) = -cos(90) = 0
tan(-750) = -tan(90) is undefined
csc(-750) = -csc(90) = -1
sec(-750) = -sec(90) is undefined
cot(-750) = -cot(90) is undefined