If a=sin1230°, b=cos(-1150°), c=tan1670°, d=cos2260°, then which of the following ordering is correct? (A) c>a>b>d (B) c>b>a>d (C) a>c>b>d (D) a>b>c>d (E) none of the above
both sin and tan are increasing functions in Quadrant I, and tan > sin
a = sin30°
b = cos70° = sin20°
c = tan50°
d = -cos80°
sure looks like c > a > b > d
How did you get to that conclusion?
To determine the correct ordering, we need to evaluate the trigonometric functions for the given angles and compare the results.
Let's start by evaluating the trigonometric functions for each angle:
a = sin(1230°)
b = cos(-1150°)
c = tan(1670°)
d = cos(2260°)
Now, let's calculate the values for each trigonometric function:
a = sin(1230°)
Using the periodicity of the sine function, we can rewrite 1230° as 1230° - 360° = 870°. The sine of 870° is equal to the sine of (870° - 360°) = 510°. The sine of 510° is equal to the sine of (510° - 360°) = 150°. The sine of 150° is 0.5. Therefore, a = 0.5.
b = cos(-1150°)
Using the periodicity of the cosine function, we can rewrite -1150° as -1150° + 360° = -790°. The cosine of -790° is equal to the cosine of (-790° + 360°) = -430°. The cosine of -430° is equal to the cosine of (-430° + 360°) = -70°. The cosine of -70° is approximately 0.342. Therefore, b ≈ 0.342.
c = tan(1670°)
Using the periodicity of the tangent function, we can rewrite 1670° as 1670° - 180° = 1490°. The tangent of 1490° is equal to the tangent of (1490° - 180°) = 1310°. The tangent of 1310° is equal to the tangent of (1310° - 180°) = 1130°. The tangent of 1130° is approximately -0.886. Therefore, c ≈ -0.886.
d = cos(2260°)
Using the periodicity of the cosine function, we can rewrite 2260° as 2260° - 360° = 1900°. The cosine of 1900° is equal to the cosine of (1900° - 360°) = 1540°. The cosine of 1540° is equal to the cosine of (1540° - 360°) = 1180°. The cosine of 1180° is approximately -0.571. Therefore, d ≈ -0.571.
Now, let's compare the values:
c ≈ -0.886
a = 0.5
b ≈ 0.342
d ≈ -0.571
Comparing the values, we see that -0.886 < 0.5 < 0.342 < -0.571.
Therefore, the correct ordering is (A) c > a > b > d.