Which of the following is/are incorrect?
(A) \(\sin 0^{\circ}=0\)
(B) \(\tan 0^{\circ}=0\)
(C) \(\cos 0^{\circ}=0\)
(D) \(\mathrm{cosec}\,0^{\circ}=0\)
(E) \(\sec 0^{\circ}=0\)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (C), (D) and (E) only
At 0° a point on the unit circle is at (1, 0), so \(\sin 0^\circ=0\) and \(\cos 0^\circ=1\); the other ratios follow from these two. The question asks for the incorrect statements.
(A) \(\sin 0^{\circ}=0\) Correct statement. At 0° the side opposite the angle shrinks to nothing, so sin 0° = 0.
(B) \(\tan 0^{\circ}=0\) Correct statement. tan 0° is sin 0° divided by cos 0°, that is, 0 ÷ 1, which is 0.
(C) \(\cos 0^{\circ}=0\) Incorrect statement. At 0° the adjacent side equals the hypotenuse, so cos 0° = 1.
(D) \(\mathrm{cosec}\,0^{\circ}=0\) Incorrect statement. cosec 0° is 1 divided by sin 0°, that is, 1 ÷ 0, which is not defined.
(E) \(\sec 0^{\circ}=0\) Incorrect statement. sec 0° is 1 divided by cos 0°, that is, 1 ÷ 1, which is 1.
Tip: At 0°, sin, tan = 0; cos, sec = 1; cosec and cot are not defined. At 90° the roles of sin and cos swap.