Online Test — Trigonometry
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
In a right-angled triangle, what is the ratio formula for the secant of an angle?
Opp / Hyp
Adj / Hyp
Hyp / Adj
Hyp / Opp
Explanation: Secant is the direct reciprocal of cosine, which is Hypotenuse / Adjacent.
Question 2 of 10
medium
Simplify the following identity-based expression: \(\sec^{2}\theta\) - \(\tan^{2}\theta\).
0
1
-1
2
Explanation: This is a direct rearrangement of the identity: 1 + tan^2 = sec^2.
Question 3 of 10
medium
If \(\cos \theta\) = 4 / 5, what is the exact fractional value of \(\cosec \theta\)?
5 / 3
3 / 5
5 / 4
4 / 3
Explanation: Opposite side is sqrt(5^2 - 4^2) = 3. cosec = Hyp / Opp = 5 / 3.
Question 4 of 10
medium
Evaluate the following standard product: sin(45°) * cos(45°).
1
1 / 2
sqrt(2)
1 / sqrt(2)
Explanation: 1/sqrt(2) multiplied by 1/sqrt(2) equals 1/2.
Question 5 of 10
medium
What is the exact value of tan(30°) multiplied by tan(60°)?
1 / 3
3
1
sqrt(3)
Explanation: (1/sqrt(3)) * sqrt(3) simplifies directly to 1.
Question 6 of 10
medium
Evaluate the numeric difference: cosec^2(45°) - cot^2(45°).
2
0
1
-1
Explanation: Since 1 + cot^2 = cosec^2, the difference cosec^2 - cot^2 always equals 1.
Question 7 of 10
medium
Evaluate the matching complementary fraction: cos(37°) / sin(53°).
0
1
tan(37°)
cot(53°)
Explanation: cos(37°) equals cos(90° - 53°) = sin(53°). The fraction equals 1.
Question 8 of 10
medium
Simplify the following expression: sin(90° - theta) * \(\sec \theta\).
1
\(\sin^{2}\theta\)
\(\cos^{2}\theta\)
\(\tan \theta\)
Explanation: sin(90° - theta) = \(\cos \theta\). \(\cos \theta\) * \(\sec \theta\) = 1.
Question 9 of 10
medium
If tan(2A) = cot(A - 18°), find the value of angle A.
18°
36°
24°
54°
Explanation: $\tan 2A = \cot(A - 18^\circ)$ gives $90^\circ - 2A = A - 18^\circ$, so $108^\circ = 3A$ and $A = 36^\circ$.
Question 10 of 10
medium
If \(\sin \theta\) + \(\cos \theta\) = sqrt(2) * \(\cos \theta\), determine the value of \(\tan \theta\).
sqrt(2) + 1
sqrt(2) - 1
1
0
Explanation: Divide by \(\cos \theta\): \(\tan \theta\) + 1 = sqrt(2) => \(\tan \theta\) = sqrt(2) - 1.