If 𝑎 = sin70°,𝑏 = cos70°,𝑐 = tan70°,𝑑 = 1 , order them from the largest to the smallest.
Superimpose the sine, the cosine, and the tangent function and look at 70°
to see that it would be
b < a < 1 < d
Or you could use your calculator and find their values,
Or ,
cosx starts at 1 and decreases with cos90° = 0
since 70 is close to 90 cos70 must be closer to 0 than 1
sinx starts at 0 and increases with sin90 = 1
since 70° is close to 90, sin70 must be closer to 1 than 0, so sin70 > cos70
neither sinx nor cosx are at 1 for x = 70, so 1 must be 3rd
tanx goes from 0 to infinitiy with tan 45° = 1
since 70 > 45, tan 70 > 1
so we have b < a < d < c
sinx = cosx at x = 45°
since sinx is increasing and cosx is decreasing, cosx < sinx at x=70°
and, since tanx > 1 for x > 45°,
cosx < sinx < tanx
oh, and since secx > tanx, add that to the list as greatest
To order 𝑎, 𝑏, 𝑐, and 𝑑 from largest to smallest, we need to evaluate their values first.
Let's calculate the values of 𝑎, 𝑏, and 𝑐 using the given trigonometric functions:
𝑎 = sin70°
𝑎 = 0.9397 (approximated value using a calculator)
𝑏 = cos70°
𝑏 = 0.3420 (approximated value using a calculator)
𝑐 = tan70°
𝑐 = 2.7475 (approximated value using a calculator)
𝑑 = 1
Now, let's compare the values:
𝑐 (2.7475) > 𝑎 (0.9397) > 𝑏 (0.3420) > 𝑑 (1)
Therefore, when ordered from largest to smallest, the values are:
𝑐 (2.7475), 𝑎 (0.9397), 𝑏 (0.3420), 𝑑 (1)