Calculate, to four decimal places, all six function values for angles that measure 34º and 56º. How are these two angles related to each other? How many of these values do you actually have to use your calculator to find? Write a paragraph that answers these questions. 1. Why are there no keys for SEC, CSC, or COT on the TI-84 and many other calculators? 2. For acute angles u, how small can sec u and csc u be? How large can these values be? 3. How are Questions 1 and 2 related?
+23254 The two angles are complementary; that is, when their sizes are added together, the sum is 90°.
From a calculator:
sin(34°) = 0.5592 sin(56°) = 0.8290
cos(34°) = 0.8290 cos(56°) = 0.5592
tan(34°) = 0.6745 tan(56°) = 1.4826
Notice that the sin(34°) = cos(56°) and vice versa.
But the tan(34°) = 1/tan(56°) and vice versa.
sec(34°) = 1/cos(34°) and sec(56°) = 1/cos(56°)
csc(34°) = 1/sin(34°) and csc(56°) = 1/sin(56°)
cot(34°) = 1/tan(34°) and cot(56°) = 1/tan(56°)
So, with the help of your calculator, you can find those decimal values; this also explains why most calculators do not contain those keys.
Since the sin can never be greater than 1 (but can be 1), the csc can never be less than 1 (but can be 1).
As the sin gets smaller and smaller, the csc gets larger and larger. At its smallest, the sin is zero; at its largest, the csc approaches an infinite size.
What is true for sin, is also true for cos.
