Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Two complementary angles are considered in this problem. a. (i) Prove that
sin
2
θ
+
sin
2
(
90
∘
−
θ
)
=
1
\sin^{2}\theta+\sin^{2}(90^{\circ}-\theta)=1
sin
2
θ
+
sin
2
(
9
0
∘
−
θ
)
=
1
for every acute angle
θ
\theta
θ
. b. (ii) If
sin
θ
=
4
5
\sin\theta=\dfrac{4}{5}
sin
θ
=
5
4
for an acute
θ
\theta
θ
, find
sin
(
90
∘
−
θ
)
\sin(90^{\circ}-\theta)
sin
(
9
0
∘
−
θ
)
and verify the result obtained in part (i) numerically.
Browse the problem library